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|00000000| 54 55 54 4f 52 20 30 36 | 6c 56 00 00 28 07 00 00 |TUTOR 06|lV..(...|
|00000010| 00 17 4f 07 0d 0b 00 4e | 6f 2e 20 20 54 68 65 20 |..O....N|o.  The |
|00000020| 11 33 79 11 31 2d 69 6e | 74 65 72 63 65 70 74 20 |.3y.1-in|tercept |
|00000030| 69 73 20 63 6f 72 72 65 | 63 74 2e 20 20 48 6f 77 |is corre|ct.  How|
|00000040| 65 76 65 72 2c 20 74 68 | 65 20 11 33 78 11 31 2d |ever, th|e .3x.1-|
|00000050| 69 6e 74 65 72 63 65 70 | 74 73 20 61 72 65 20 77 |intercep|ts are w|
|00000060| 72 6f 6e 67 2e 20 20 0d | 0a 00 20 20 20 20 20 20 |rong.  .|..      |
|00000070| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000080| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000090| 20 20 20 20 20 20 11 32 | 32 0d 0b 00 11 31 4c 65 |      .2|2....1Le|
|000000a0| 74 74 69 6e 67 20 11 33 | 79 20 11 31 62 65 20 30 |tting .3|y .1be 0|
|000000b0| 2c 20 77 65 20 6f 62 74 | 61 69 6e 20 74 68 65 20 |, we obt|ain the |
|000000c0| 65 71 75 61 74 69 6f 6e | 20 30 20 3d 20 11 33 78 |equation| 0 = .3x|
|000000d0| 20 20 11 31 2b 20 34 11 | 33 78 20 11 31 2d 20 35 |  .1+ 4.|3x .1- 5|
|000000e0| 2c 20 77 68 69 63 68 20 | 66 61 63 74 6f 72 73 20 |, which |factors |
|000000f0| 61 73 20 0d 0a 00 0d 0b | 00 30 20 3d 20 28 11 33 |as .....|.0 = (.3|
|00000100| 78 20 11 31 2b 20 35 29 | 28 11 33 78 20 11 31 2d |x .1+ 5)|(.3x .1-|
|00000110| 20 31 29 2e 20 20 53 65 | 74 74 69 6e 67 20 65 61 | 1).  Se|tting ea|
|00000120| 63 68 20 66 61 63 74 6f | 72 20 65 71 75 61 6c 20 |ch facto|r equal |
|00000130| 74 6f 20 30 20 61 6e 64 | 20 73 6f 6c 76 69 6e 67 |to 0 and| solving|
|00000140| 20 66 6f 72 20 11 33 78 | 11 31 2c 20 77 65 0d 0a | for .3x|.1, we..|
|00000150| 00 0d 0b 00 6f 62 74 61 | 69 6e 20 11 33 78 20 11 |....obta|in .3x .|
|00000160| 31 3d 20 2d 35 20 61 6e | 64 20 11 33 78 20 11 31 |1= -5 an|d .3x .1|
|00000170| 3d 20 31 2e 20 20 54 68 | 75 73 2c 20 74 68 65 20 |= 1.  Th|us, the |
|00000180| 11 33 78 11 31 2d 69 6e | 74 65 72 63 65 70 74 73 |.3x.1-in|tercepts|
|00000190| 20 61 72 65 20 28 2d 35 | 2c 20 30 29 20 61 6e 64 | are (-5|, 0) and|
|000001a0| 20 28 31 2c 20 30 29 2e | 0d 0a 00 00 17 4f 07 0d | (1, 0).|.....O..|
|000001b0| 0b 00 57 72 6f 6e 67 2e | 20 20 4c 65 74 74 69 6e |..Wrong.|  Lettin|
|000001c0| 67 20 11 33 78 20 11 31 | 3d 20 30 2c 20 77 65 20 |g .3x .1|= 0, we |
|000001d0| 6f 62 74 61 69 6e 20 11 | 33 79 20 11 31 3d 20 2d |obtain .|3y .1= -|
|000001e0| 35 2e 20 20 54 68 75 73 | 2c 20 74 68 65 20 11 33 |5.  Thus|, the .3|
|000001f0| 79 11 31 2d 69 6e 74 65 | 72 63 65 70 74 20 69 73 |y.1-inte|rcept is|
|00000200| 20 28 30 2c 20 2d 35 29 | 2e 0d 0a 00 20 20 20 20 | (0, -5)|....    |
|00000210| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000220| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000230| 20 20 20 20 20 20 20 20 | 11 32 32 0d 0b 00 11 31 |        |.22....1|
|00000240| 4c 65 74 74 69 6e 67 20 | 11 33 79 20 11 31 62 65 |Letting |.3y .1be|
|00000250| 20 30 2c 20 77 65 20 6f | 62 74 61 69 6e 20 74 68 | 0, we o|btain th|
|00000260| 65 20 65 71 75 61 74 69 | 6f 6e 20 30 20 3d 20 11 |e equati|on 0 = .|
|00000270| 33 78 20 20 11 31 2b 20 | 34 11 33 78 20 11 31 2d |3x  .1+ |4.3x .1-|
|00000280| 20 35 2c 20 77 68 69 63 | 68 20 66 61 63 74 6f 72 | 5, whic|h factor|
|00000290| 73 20 61 73 20 0d 0a 00 | 0d 0b 00 30 20 3d 20 28 |s as ...|...0 = (|
|000002a0| 11 33 78 20 11 31 2b 20 | 35 29 28 11 33 78 20 11 |.3x .1+ |5)(.3x .|
|000002b0| 31 2d 20 31 29 2e 20 20 | 53 65 74 74 69 6e 67 20 |1- 1).  |Setting |
|000002c0| 65 61 63 68 20 66 61 63 | 74 6f 72 20 65 71 75 61 |each fac|tor equa|
|000002d0| 6c 20 74 6f 20 30 20 61 | 6e 64 20 73 6f 6c 76 69 |l to 0 a|nd solvi|
|000002e0| 6e 67 20 66 6f 72 20 11 | 33 78 11 31 2c 20 77 65 |ng for .|3x.1, we|
|000002f0| 0d 0a 00 0d 0b 00 6f 62 | 74 61 69 6e 20 11 33 78 |......ob|tain .3x|
|00000300| 20 11 31 3d 20 2d 35 20 | 61 6e 64 20 11 33 78 20 | .1= -5 |and .3x |
|00000310| 11 31 3d 20 31 2e 20 20 | 54 68 75 73 2c 20 74 68 |.1= 1.  |Thus, th|
|00000320| 65 20 11 33 78 11 31 2d | 69 6e 74 65 72 63 65 70 |e .3x.1-|intercep|
|00000330| 74 73 20 61 72 65 20 28 | 2d 35 2c 20 30 29 20 61 |ts are (|-5, 0) a|
|00000340| 6e 64 20 28 31 2c 20 30 | 29 2e 0d 0a 00 00 17 4f |nd (1, 0|)......O|
|00000350| 07 0d 0b 00 57 72 6f 6e | 67 2e 20 20 4c 65 74 74 |....Wron|g.  Lett|
|00000360| 69 6e 67 20 11 33 78 20 | 11 31 3d 20 30 2c 20 77 |ing .3x |.1= 0, w|
|00000370| 65 20 6f 62 74 61 69 6e | 20 11 33 79 20 11 31 3d |e obtain| .3y .1=|
|00000380| 20 2d 35 2e 20 20 54 68 | 75 73 2c 20 74 68 65 20 | -5.  Th|us, the |
|00000390| 11 33 79 11 31 2d 69 6e | 74 65 72 63 65 70 74 20 |.3y.1-in|tercept |
|000003a0| 69 73 20 28 30 2c 20 2d | 35 29 2e 0d 0a 00 20 20 |is (0, -|5)....  |
|000003b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000003c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000003d0| 20 20 20 20 20 20 20 20 | 20 20 11 32 32 0d 0b 00 |        |  .22...|
|000003e0| 11 31 4c 65 74 74 69 6e | 67 20 11 33 79 20 11 31 |.1Lettin|g .3y .1|
|000003f0| 62 65 20 30 2c 20 77 65 | 20 6f 62 74 61 69 6e 20 |be 0, we| obtain |
|00000400| 74 68 65 20 65 71 75 61 | 74 69 6f 6e 20 30 20 3d |the equa|tion 0 =|
|00000410| 20 11 33 78 20 20 11 31 | 2b 20 34 11 33 78 20 11 | .3x  .1|+ 4.3x .|
|00000420| 31 2d 20 35 2c 20 77 68 | 69 63 68 20 66 61 63 74 |1- 5, wh|ich fact|
|00000430| 6f 72 73 20 61 73 20 0d | 0a 00 0d 0b 00 30 20 3d |ors as .|.....0 =|
|00000440| 20 28 11 33 78 20 11 31 | 2b 20 35 29 28 11 33 78 | (.3x .1|+ 5)(.3x|
|00000450| 20 11 31 2d 20 31 29 2e | 20 20 53 65 74 74 69 6e | .1- 1).|  Settin|
|00000460| 67 20 65 61 63 68 20 66 | 61 63 74 6f 72 20 65 71 |g each f|actor eq|
|00000470| 75 61 6c 20 74 6f 20 30 | 20 61 6e 64 20 73 6f 6c |ual to 0| and sol|
|00000480| 76 69 6e 67 20 66 6f 72 | 20 11 33 78 11 31 2c 20 |ving for| .3x.1, |
|00000490| 77 65 0d 0a 00 0d 0b 00 | 6f 62 74 61 69 6e 20 11 |we......|obtain .|
|000004a0| 33 78 20 11 31 3d 20 2d | 35 20 61 6e 64 20 11 33 |3x .1= -|5 and .3|
|000004b0| 78 20 11 31 3d 20 31 2e | 20 20 54 68 75 73 2c 20 |x .1= 1.|  Thus, |
|000004c0| 74 68 65 20 11 33 78 11 | 31 2d 69 6e 74 65 72 63 |the .3x.|1-interc|
|000004d0| 65 70 74 73 20 61 72 65 | 20 28 2d 35 2c 20 30 29 |epts are| (-5, 0)|
|000004e0| 20 61 6e 64 20 28 31 2c | 20 30 29 2e 0d 0a 00 00 | and (1,| 0).....|
|000004f0| 17 4f 04 0d 0b 00 52 69 | 67 68 74 2e 20 20 54 68 |.O....Ri|ght.  Th|
|00000500| 65 73 65 20 61 72 65 20 | 74 68 65 20 11 33 78 11 |ese are |the .3x.|
|00000510| 31 2d 20 61 6e 64 20 11 | 33 79 11 31 2d 69 6e 74 |1- and .|3y.1-int|
|00000520| 65 72 63 65 70 74 73 20 | 6f 66 20 74 68 65 20 67 |ercepts |of the g|
|00000530| 72 61 70 68 20 6f 66 20 | 74 68 65 20 67 69 76 65 |raph of |the give|
|00000540| 6e 20 0d 0a 00 65 71 75 | 61 74 69 6f 6e 2e 0d 0a |n ...equ|ation...|
|00000550| 00 00 17 4f 05 0d 0b 00 | 57 72 6f 6e 67 2e 20 20 |...O....|Wrong.  |
|00000560| 54 68 65 20 11 33 78 11 | 31 2d 69 6e 74 65 72 63 |The .3x.|1-interc|
|00000570| 65 70 74 20 69 73 20 63 | 6f 72 72 65 63 74 2c 20 |ept is c|orrect, |
|00000580| 62 75 74 20 74 68 65 20 | 11 33 79 11 31 2d 69 6e |but the |.3y.1-in|
|00000590| 74 65 72 63 65 70 74 20 | 69 73 20 6e 6f 74 2e 20 |tercept |is not. |
|000005a0| 20 4c 65 74 74 69 6e 67 | 20 0d 0a 00 11 33 78 20 | Letting| ....3x |
|000005b0| 11 31 3d 20 30 2c 20 77 | 65 20 77 61 6e 74 20 74 |.1= 0, w|e want t|
|000005c0| 6f 20 73 6f 6c 76 65 20 | 32 11 33 79 20 11 31 2d |o solve |2.3y .1-|
|000005d0| 20 33 20 3d 20 30 20 66 | 6f 72 20 11 33 79 11 31 | 3 = 0 f|or .3y.1|
|000005e0| 2e 20 20 41 66 74 65 72 | 20 73 6f 6c 76 69 6e 67 |.  After| solving|
|000005f0| 2c 20 77 65 20 6f 62 74 | 61 69 6e 20 74 68 65 20 |, we obt|ain the |
|00000600| 0d 0a 00 73 6f 6c 75 74 | 69 6f 6e 20 11 33 79 20 |...solut|ion .3y |
|00000610| 11 31 3d 20 33 2f 32 2e | 20 20 54 68 75 73 2c 20 |.1= 3/2.|  Thus, |
|00000620| 74 68 65 20 11 33 79 11 | 31 2d 69 6e 74 65 72 63 |the .3y.|1-interc|
|00000630| 65 70 74 20 69 73 20 61 | 74 20 28 30 2c 20 33 2f |ept is a|t (0, 3/|
|00000640| 32 29 2e 0d 0a 00 00 17 | 4f 06 0d 0b 00 57 72 6f |2)......|O....Wro|
|00000650| 6e 67 2e 20 20 4c 65 74 | 74 69 6e 67 20 11 33 79 |ng.  Let|ting .3y|
|00000660| 20 11 31 3d 20 30 2c 20 | 77 65 20 77 61 6e 74 20 | .1= 0, |we want |
|00000670| 74 6f 20 73 6f 6c 76 65 | 20 2d 11 33 78 20 11 31 |to solve| -.3x .1|
|00000680| 2d 20 33 20 3d 20 30 20 | 66 6f 72 20 11 33 78 11 |- 3 = 0 |for .3x.|
|00000690| 31 2e 20 20 41 66 74 65 | 72 20 73 6f 6c 76 69 6e |1.  Afte|r solvin|
|000006a0| 67 2c 20 0d 0a 00 77 65 | 20 6f 62 74 61 69 6e 20 |g, ...we| obtain |
|000006b0| 11 33 78 20 11 31 3d 20 | 2d 33 20 66 6f 72 20 61 |.3x .1= |-3 for a|
|000006c0| 6e 20 11 33 78 11 31 2d | 69 6e 74 65 72 63 65 70 |n .3x.1-|intercep|
|000006d0| 74 20 61 74 20 28 2d 33 | 2c 20 30 29 2e 20 20 4c |t at (-3|, 0).  L|
|000006e0| 65 74 74 69 6e 67 20 11 | 33 78 20 11 31 3d 20 30 |etting .|3x .1= 0|
|000006f0| 2c 20 77 65 20 73 6f 6c | 76 65 20 0d 0a 00 32 11 |, we sol|ve ...2.|
|00000700| 33 79 20 11 31 2d 20 33 | 20 3d 20 30 20 66 6f 72 |3y .1- 3| = 0 for|
|00000710| 20 11 33 79 11 31 2e 20 | 20 41 66 74 65 72 20 73 | .3y.1. | After s|
|00000720| 6f 6c 76 69 6e 67 2c 20 | 77 65 20 6f 62 74 61 69 |olving, |we obtai|
|00000730| 6e 20 11 33 79 20 11 31 | 3d 20 33 2f 32 2e 20 20 |n .3y .1|= 3/2.  |
|00000740| 54 68 75 73 2c 20 74 68 | 65 20 0d 0a 00 11 33 79 |Thus, th|e ....3y|
|00000750| 11 31 2d 69 6e 74 65 72 | 63 65 70 74 20 69 73 20 |.1-inter|cept is |
|00000760| 61 74 20 28 30 2c 20 33 | 2f 32 29 2e 0d 0a 00 00 |at (0, 3|/2).....|
|00000770| 17 4f 03 0d 0b 00 52 69 | 67 68 74 2e 20 20 54 68 |.O....Ri|ght.  Th|
|00000780| 65 73 65 20 61 72 65 20 | 74 68 65 20 69 6e 74 65 |ese are |the inte|
|00000790| 72 63 65 70 74 73 20 6f | 66 20 74 68 65 20 67 72 |rcepts o|f the gr|
|000007a0| 61 70 68 20 6f 66 20 74 | 68 65 20 67 69 76 65 6e |aph of t|he given|
|000007b0| 20 65 71 75 61 74 69 6f | 6e 2e 0d 0a 00 00 17 4f | equatio|n......O|
|000007c0| 03 0d 0b 00 4e 6f 2e 20 | 20 43 68 65 63 6b 20 79 |....No. | Check y|
|000007d0| 6f 75 72 20 77 6f 72 6b | 2e 20 20 54 68 65 20 63 |our work|.  The c|
|000007e0| 6f 72 72 65 63 74 20 69 | 6e 74 65 72 63 65 70 74 |orrect i|ntercept|
|000007f0| 73 20 61 72 65 20 28 2d | 33 2c 20 30 29 20 61 6e |s are (-|3, 0) an|
|00000800| 64 20 28 30 2c 20 33 2f | 32 29 2e 0d 0a 00 00 17 |d (0, 3/|2)......|
|00000810| 4f 0a 0d 0b 00 57 72 6f | 6e 67 2e 20 20 54 6f 20 |O....Wro|ng.  To |
|00000820| 73 65 65 20 77 68 79 20 | 6e 6f 74 2c 20 77 65 20 |see why |not, we |
|00000830| 72 65 70 6c 61 63 65 20 | 11 33 78 20 11 31 77 69 |replace |.3x .1wi|
|00000840| 74 68 20 2d 11 33 78 20 | 11 31 61 73 20 66 6f 6c |th -.3x |.1as fol|
|00000850| 6c 6f 77 73 2e 12 30 0d | 0a 00 20 20 20 20 20 20 |lows..0.|..      |
|00000860| 20 20 20 20 11 32 32 0d | 0b 00 20 20 20 20 11 31 |    .22.|..    .1|
|00000870| 2d 11 33 78 20 11 31 2b | 20 11 33 79 20 20 11 31 |-.3x .1+| .3y  .1|
|00000880| 3d 20 30 20 20 20 20 20 | 20 20 20 20 20 20 11 32 |= 0     |      .2|
|00000890| 12 31 47 69 76 65 6e 20 | 65 71 75 61 74 69 6f 6e |.1Given |equation|
|000008a0| 12 30 0d 0a 00 20 20 20 | 20 20 20 20 20 20 20 32 |.0...   |       2|
|000008b0| 0d 0b 00 20 11 31 2d 28 | 2d 11 33 78 11 31 29 20 |... .1-(|-.3x.1) |
|000008c0| 2b 20 11 33 79 20 20 11 | 31 3d 20 30 20 20 20 20 |+ .3y  .|1= 0    |
|000008d0| 20 20 20 20 20 20 20 11 | 32 12 31 52 65 70 6c 61 |       .|2.1Repla|
|000008e0| 63 65 20 78 20 77 69 74 | 68 20 2d 78 12 30 0d 0a |ce x wit|h -x.0..|
|000008f0| 00 20 20 20 20 20 20 20 | 20 20 20 32 0d 0b 00 20 |.       |   2... |
|00000900| 20 20 20 20 11 33 78 20 | 11 31 2b 20 11 33 79 20 |    .3x |.1+ .3y |
|00000910| 20 11 31 3d 20 30 20 20 | 20 20 20 20 20 20 20 20 | .1= 0  |        |
|00000920| 20 11 32 12 31 52 65 70 | 6c 61 63 65 6d 65 6e 74 | .2.1Rep|lacement|
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|00000950| 75 61 74 69 6f 6e 12 30 | 0d 0a 00 0d 0b 00 11 31 |uation.0|.......1|
|00000960| 12 30 53 69 6e 63 65 20 | 74 68 65 20 72 65 70 6c |.0Since |the repl|
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|00000980| 20 79 69 65 6c 64 20 61 | 6e 20 65 71 75 69 76 61 | yield a|n equiva|
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|000009a0| 65 20 63 6f 6e 63 6c 75 | 64 65 0d 0a 00 74 68 61 |e conclu|de...tha|
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|000009c0| 74 69 6f 6e 20 69 73 20 | 6e 6f 74 20 73 79 6d 6d |tion is |not symm|
|000009d0| 65 74 72 69 63 20 77 69 | 74 68 20 72 65 73 70 65 |etric wi|th respe|
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|000009f0| 61 78 69 73 2e 0d 0a 00 | 00 17 4f 04 0d 0b 00 47 |axis....|..O....G|
|00000a00| 6f 6f 64 20 6a 6f 62 2e | 20 20 53 69 6e 63 65 20 |ood job.|  Since |
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|00000a20| 69 76 61 6c 65 6e 74 20 | 65 71 75 61 74 69 6f 6e |ivalent |equation|
|00000a30| 20 61 66 74 65 72 20 72 | 65 70 6c 61 63 69 6e 67 | after r|eplacing|
|00000a40| 20 11 33 79 20 11 31 62 | 79 20 2d 11 33 79 11 31 | .3y .1b|y -.3y.1|
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|00000a60| 74 68 61 74 20 74 68 65 | 20 67 69 76 65 6e 20 65 |that the| given e|
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|00000a90| 74 20 74 6f 20 74 68 65 | 20 11 33 78 11 31 2d 61 |t to the| .3x.1-a|
|00000aa0| 78 69 73 2e 0d 0a 00 00 | 17 4f 09 0d 0b 00 57 72 |xis.....|.O....Wr|
|00000ab0| 6f 6e 67 2e 20 20 54 6f | 20 73 65 65 20 77 68 79 |ong.  To| see why|
|00000ac0| 20 6e 6f 74 2c 20 72 65 | 70 6c 61 63 65 20 11 33 | not, re|place .3|
|00000ad0| 78 20 11 31 62 79 20 2d | 11 33 78 20 11 31 61 6e |x .1by -|.3x .1an|
|00000ae0| 64 20 11 33 79 20 11 31 | 62 79 20 2d 11 33 79 11 |d .3y .1|by -.3y.|
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|00000b00| 20 20 20 20 20 32 0d 0b | 00 20 20 20 20 20 20 11 |     2..|.      .|
|00000b10| 31 2d 11 33 78 20 11 31 | 2b 20 11 33 79 20 20 11 |1-.3x .1|+ .3y  .|
|00000b20| 31 3d 20 30 20 20 20 20 | 20 20 20 20 20 11 32 12 |1= 0    |     .2.|
|00000b30| 31 47 69 76 65 6e 20 65 | 71 75 61 74 69 6f 6e 12 |1Given e|quation.|
|00000b40| 30 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |0...    |        |
|00000b50| 32 0d 0b 00 11 31 2d 28 | 2d 11 33 78 11 31 29 20 |2....1-(|-.3x.1) |
|00000b60| 2b 20 28 2d 11 33 79 11 | 31 29 20 20 3d 20 30 20 |+ (-.3y.|1)  = 0 |
|00000b70| 20 20 20 20 20 20 20 20 | 11 32 12 31 52 65 70 6c |        |.2.1Repl|
|00000b80| 61 63 65 20 78 20 62 79 | 20 2d 78 20 61 6e 64 20 |ace x by| -x and |
|00000b90| 79 20 62 79 20 2d 79 12 | 30 0d 0a 00 20 20 20 20 |y by -y.|0...    |
|00000ba0| 20 20 20 20 20 20 20 20 | 32 0d 0b 00 20 20 20 20 |        |2...    |
|00000bb0| 20 20 20 11 33 78 20 11 | 31 2b 20 11 33 79 20 20 |   .3x .|1+ .3y  |
|00000bc0| 11 31 3d 20 30 20 20 20 | 20 20 20 20 20 20 11 32 |.1= 0   |      .2|
|00000bd0| 12 31 52 65 70 6c 61 63 | 65 6d 65 6e 74 20 64 6f |.1Replac|ement do|
|00000be0| 65 73 20 6e 6f 74 20 79 | 69 65 6c 64 20 61 6e 20 |es not y|ield an |
|00000bf0| 65 71 75 69 76 61 6c 65 | 6e 74 20 65 71 75 61 74 |equivale|nt equat|
|00000c00| 69 6f 6e 12 30 0d 0a 00 | 0d 0b 00 11 31 12 30 53 |ion.0...|....1.0S|
|00000c10| 69 6e 63 65 20 74 68 65 | 20 72 65 70 6c 61 63 65 |ince the| replace|
|00000c20| 6d 65 6e 74 20 64 6f 65 | 73 20 6e 6f 74 20 79 69 |ment doe|s not yi|
|00000c30| 65 6c 64 20 61 6e 20 65 | 71 75 69 76 61 6c 65 6e |eld an e|quivalen|
|00000c40| 74 20 65 71 75 61 74 69 | 6f 6e 2c 20 77 65 20 63 |t equati|on, we c|
|00000c50| 6f 6e 63 6c 75 64 65 0d | 0a 00 74 68 61 74 20 74 |onclude.|..that t|
|00000c60| 68 65 20 67 69 76 65 6e | 20 65 71 75 61 74 69 6f |he given| equatio|
|00000c70| 6e 20 69 73 20 6e 6f 74 | 20 73 79 6d 6d 65 74 72 |n is not| symmetr|
|00000c80| 69 63 20 77 69 74 68 20 | 72 65 73 70 65 63 74 20 |ic with |respect |
|00000c90| 74 6f 20 74 68 65 20 6f | 72 69 67 69 6e 2e 0d 0a |to the o|rigin...|
|00000ca0| 00 00 17 4f 09 0d 0b 00 | 57 72 6f 6e 67 2e 20 20 |...O....|Wrong.  |
|00000cb0| 54 68 65 20 67 72 61 70 | 68 20 6f 66 20 74 68 65 |The grap|h of the|
|00000cc0| 20 67 69 76 65 6e 20 65 | 71 75 61 74 69 6f 6e 20 | given e|quation |
|00000cd0| 69 73 20 73 79 6d 6d 65 | 74 72 69 63 20 74 6f 20 |is symme|tric to |
|00000ce0| 74 68 65 20 11 33 78 11 | 31 2d 61 78 69 73 2e 12 |the .3x.|1-axis..|
|00000cf0| 30 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 11 32 |0...    |      .2|
|00000d00| 32 0d 0b 00 20 20 20 20 | 11 31 2d 11 33 78 20 11 |2...    |.1-.3x .|
|00000d10| 31 2b 20 11 33 79 20 20 | 11 31 3d 20 30 20 20 20 |1+ .3y  |.1= 0   |
|00000d20| 20 20 20 20 20 20 20 20 | 20 11 32 12 31 47 69 76 |        | .2.1Giv|
|00000d30| 65 6e 20 65 71 75 61 74 | 69 6f 6e 12 30 0d 0a 00 |en equat|ion.0...|
|00000d40| 20 20 20 20 20 20 20 20 | 20 20 32 0d 0b 00 20 11 |        |  2... .|
|00000d50| 31 2d 11 33 78 20 11 31 | 2b 20 28 2d 11 33 79 11 |1-.3x .1|+ (-.3y.|
|00000d60| 31 29 20 20 3d 20 30 20 | 20 20 20 20 20 20 20 20 |1)  = 0 |        |
|00000d70| 20 20 20 11 32 12 31 52 | 65 70 6c 61 63 65 20 79 |   .2.1R|eplace y|
|00000d80| 20 62 79 20 2d 79 12 30 | 0d 0a 00 20 20 20 20 20 | by -y.0|...     |
|00000d90| 20 20 20 20 20 32 0d 0b | 00 20 20 20 20 11 31 2d |     2..|.    .1-|
|00000da0| 11 33 78 20 11 31 2b 20 | 11 33 79 20 20 11 31 3d |.3x .1+ |.3y  .1=|
|00000db0| 20 30 20 20 20 20 20 20 | 20 20 20 20 20 20 11 32 | 0      |      .2|
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|00000e70| 20 74 6f 20 74 68 65 20 | 11 33 78 11 31 2d 61 78 | to the |.3x.1-ax|
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|00000ea0| 6e 6f 74 2c 20 77 65 20 | 72 65 70 6c 61 63 65 20 |not, we |replace |
|00000eb0| 11 33 78 20 11 31 77 69 | 74 68 20 2d 11 33 78 20 |.3x .1wi|th -.3x |
|00000ec0| 11 31 61 73 20 66 6f 6c | 6c 6f 77 73 2e 12 30 0d |.1as fol|lows..0.|
|00000ed0| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 11 32 32 |..      |     .22|
|00000ee0| 0d 0b 00 20 20 20 20 20 | 20 20 11 31 28 2d 11 33 |...     |  .1(-.3|
|00000ef0| 78 11 31 29 20 20 2d 20 | 33 0d 0b 00 20 20 20 11 |x.1)  - |3...   .|
|00000f00| 33 79 20 11 31 3d 20 11 | 34 32 32 32 32 32 32 32 |3y .1= .|42222222|
|00000f10| 32 32 20 20 20 20 20 20 | 20 20 20 20 11 32 12 31 |22      |    .2.1|
|00000f20| 52 65 70 6c 61 63 65 20 | 78 20 77 69 74 68 20 2d |Replace |x with -|
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|00000f50| 20 11 31 32 28 2d 11 33 | 78 11 31 29 0d 0a 00 20 | .12(-.3|x.1)... |
|00000f60| 20 20 20 20 20 20 20 20 | 11 32 32 0d 0b 00 20 20 |        |.22...  |
|00000f70| 20 20 20 20 20 20 11 33 | 78 20 20 11 31 2d 20 33 |      .3|x  .1- 3|
|00000f80| 0d 0b 00 20 20 20 11 33 | 79 20 11 31 3d 20 2d 11 |...   .3|y .1= -.|
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|00000fa0| 20 20 20 11 32 12 31 52 | 65 70 6c 61 63 65 6d 65 |   .2.1R|eplaceme|
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|000010c0| 68 20 2d 11 33 79 20 11 | 31 61 73 20 66 6f 6c 6c |h -.3y .|1as foll|
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|000010f0| 11 33 78 20 20 11 31 2d | 20 33 0d 0b 00 20 28 2d |.3x  .1-| 3... (-|
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|00001110| 32 20 20 20 20 20 20 20 | 20 20 20 20 20 11 32 12 |2       |     .2.|
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|00001140| 74 69 6f 6e 12 30 0d 0b | 00 20 20 20 20 20 20 20 |tion.0..|.       |
|00001150| 20 20 20 11 31 32 11 33 | 78 0d 0a 00 20 20 20 20 |   .12.3|x...    |
|00001160| 20 20 20 20 11 32 32 0d | 0b 00 20 20 20 20 20 20 |    .22.|..      |
|00001170| 20 11 33 78 20 20 11 31 | 2d 20 33 0d 0b 00 20 20 | .3x  .1|- 3...  |
|00001180| 2d 11 33 79 20 11 31 3d | 20 11 34 32 32 32 32 32 |-.3y .1=| .422222|
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|00001290| 6f 64 20 6a 6f 62 2e 20 | 20 53 69 6e 63 65 20 77 |od job. | Since w|
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|000012b0| 76 61 6c 65 6e 74 20 65 | 71 75 61 74 69 6f 6e 20 |valent e|quation |
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|00001350| 00 57 72 6f 6e 67 2e 20 | 20 54 68 65 20 67 72 61 |.Wrong. | The gra|
|00001360| 70 68 20 6f 66 20 74 68 | 65 20 67 69 76 65 6e 20 |ph of th|e given |
|00001370| 65 71 75 61 74 69 6f 6e | 20 69 73 20 73 79 6d 6d |equation| is symm|
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|000013a0| 20 20 20 20 20 20 11 32 | 32 0d 0b 00 20 20 20 20 |      .2|2...    |
|000013b0| 20 20 20 11 31 28 2d 11 | 33 78 11 31 29 20 20 2d |   .1(-.|3x.1)  -|
|000013c0| 20 33 0d 0b 00 28 2d 11 | 33 79 11 31 29 20 3d 20 | 3...(-.|3y.1) = |
|000013d0| 11 34 32 32 32 32 32 32 | 32 32 32 20 20 20 20 20 |.4222222|222     |
|000013e0| 20 20 20 20 20 11 32 12 | 31 52 65 70 6c 61 63 65 |     .2.|1Replace|
|000013f0| 20 78 20 77 69 74 68 20 | 2d 78 20 61 6e 64 20 79 | x with |-x and y|
|00001400| 20 77 69 74 68 20 2d 79 | 20 69 6e 20 67 69 76 65 | with -y| in give|
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|00001420| 20 20 20 20 20 20 20 20 | 11 31 32 28 2d 11 33 78 |        |.12(-.3x|
|00001430| 11 31 29 0d 0a 00 20 20 | 20 20 20 20 20 20 20 11 |.1)...  |       .|
|00001440| 32 32 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |22      |        |
|00001450| 20 20 20 20 32 0d 0b 00 | 20 20 20 20 20 20 20 20 |    2...|        |
|00001460| 11 33 78 20 20 11 31 2d | 20 33 20 20 20 20 20 20 |.3x  .1-| 3      |
|00001470| 20 20 20 20 20 20 20 11 | 33 78 20 20 11 31 2d 20 |       .|3x  .1- |
|00001480| 33 0d 0b 00 20 20 2d 11 | 33 79 20 11 31 3d 20 2d |3...  -.|3y .1= -|
|00001490| 11 34 32 32 32 32 32 32 | 20 20 20 35 35 36 20 20 |.4222222|   556  |
|000014a0| 20 11 33 79 20 11 31 3d | 20 11 34 32 32 32 32 32 | .3y .1=| .422222|
|000014b0| 32 20 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 11 |2 ...   |       .|
|000014c0| 31 32 11 33 78 20 20 20 | 20 20 20 20 20 20 20 20 |12.3x   |        |
|000014d0| 20 20 20 20 20 20 11 31 | 32 11 33 78 0d 0a 00 0d |      .1|2.3x....|
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|00001560| 74 20 74 6f 20 74 68 65 | 20 11 33 78 11 31 2d 61 |t to the| .3x.1-a|
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|00001710| 2c 20 77 65 20 68 61 76 | 65 20 11 33 79 20 11 31 |, we hav|e .3y .1|
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|00001930| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001940| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001950| 20 20 20 20 20 20 20 20 | 20 20 11 32 32 0d 0b 00 |        |  .22...|
|00001960| 11 33 78 11 31 2d 69 6e | 74 65 72 63 65 70 74 2e |.3x.1-in|tercept.|
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|000019c0| 20 28 11 33 78 20 11 31 | 2d 20 33 29 28 11 33 78 | (.3x .1|- 3)(.3x|
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|00001a70| 0a 00 0d 0b 00 61 6e 64 | 20 28 31 2c 20 30 29 2e |.....and| (1, 0).|
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|00001aa0| 0d 0a 00 00 17 4f 03 0d | 0b 00 57 72 6f 6e 67 2e |.....O..|..Wrong.|
|00001ab0| 20 20 4f 6e 65 20 6f 66 | 20 74 68 65 20 61 62 6f |  One of| the abo|
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|00001ad0| 54 72 79 20 61 67 61 69 | 6e 2e 0d 0a 00 00 17 4f |Try agai|n......O|
|00001ae0| 08 0d 0b 00 57 72 6f 6e | 67 2e 20 20 54 68 65 20 |....Wron|g.  The |
|00001af0| 67 72 61 70 68 20 6f 66 | 20 74 68 65 20 67 69 76 |graph of| the giv|
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|00001b10| 20 6e 6f 74 20 70 61 73 | 73 20 74 68 72 6f 75 67 | not pas|s throug|
|00001b20| 68 20 28 30 2c 20 30 29 | 2e 20 20 4c 65 74 0d 0a |h (0, 0)|.  Let..|
|00001b30| 00 11 33 78 20 11 31 3d | 20 30 20 74 6f 20 6f 62 |..3x .1=| 0 to ob|
|00001b40| 74 61 69 6e 20 11 33 79 | 20 11 31 3d 20 32 2e 20 |tain .3y| .1= 2. |
|00001b50| 20 54 68 75 73 2c 20 74 | 68 65 20 11 33 79 11 31 | Thus, t|he .3y.1|
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|00001ba0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00001bd0| 20 20 20 20 20 20 20 20 | 20 20 11 32 33 20 20 20 |        |  .23   |
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|00001bf0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00001e30| 20 20 20 11 32 33 11 34 | 66 20 20 20 20 20 20 20 |   .23.4|f       |
|00001e40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00001e60| 11 32 33 11 34 66 20 20 | 20 20 21 0d 0b 00 11 33 |.23.4f  |  !....3|
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|00001ea0| 70 74 20 61 74 20 11 34 | 21 11 31 2d 11 34 76 20 |pt at .4|!.1-.4v |
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|00001ef0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |        |       .|
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|00002790| 00 00 17 4f 04 0d 0b 00 | 4e 6f 74 20 71 75 69 74 |...O....|Not quit|
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|00002940| 20 20 20 20 20 20 20 20 | 20 12 30 0d 0a 00 20 20 |        | .0...  |
|00002950| 20 20 20 20 20 20 20 20 | 20 11 34 67 32 32 32 32 |        | .4g2222|
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|00002970| 32 20 20 20 20 20 67 32 | 32 32 32 32 20 20 20 20 |2     g2|2222    |
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|00002990| 66 20 20 20 20 20 20 20 | 20 20 20 11 32 32 20 20 |f       |   .22  |
|000029a0| 20 20 20 20 20 20 20 20 | 32 20 20 20 20 11 34 66 |        |2    .4f|
|000029b0| 20 20 20 20 20 20 20 20 | 20 20 66 0d 0b 00 20 20 |        |  f...  |
|000029c0| 20 20 20 11 33 72 20 11 | 31 3d 20 11 34 76 20 11 |   .3r .|1= .4v .|
|000029d0| 31 5b 30 20 2d 20 28 2d | 33 29 5d 20 20 2b 20 28 |1[0 - (-|3)]  + (|
|000029e0| 30 20 2d 20 34 29 20 20 | 3d 20 11 34 76 20 11 31 |0 - 4)  |= .4v .1|
|000029f0| 39 20 2b 20 31 36 20 3d | 20 11 34 76 20 11 31 32 |9 + 16 =| .4v .12|
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|00002a10| 68 20 74 68 65 20 63 65 | 6e 74 65 72 20 28 11 33 |h the ce|nter (.3|
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|00002a30| 33 2c 20 34 29 20 61 6e | 64 20 74 68 65 20 72 61 |3, 4) an|d the ra|
|00002a40| 64 69 75 73 20 11 33 72 | 20 11 31 3d 20 35 2c 20 |dius .3r| .1= 5, |
|00002a50| 77 65 20 77 72 69 74 65 | 20 74 68 65 20 0d 0a 00 |we write| the ...|
|00002a60| 73 74 61 6e 64 61 72 64 | 20 66 6f 72 6d 20 6f 66 |standard| form of|
|00002a70| 20 74 68 65 20 65 71 75 | 61 74 69 6f 6e 20 6f 66 | the equ|ation of|
|00002a80| 20 74 68 65 20 63 69 72 | 63 6c 65 20 61 73 20 66 | the cir|cle as f|
|00002a90| 6f 6c 6c 6f 77 73 2e 12 | 30 0d 0a 00 20 20 20 20 |ollows..|0...    |
|00002aa0| 20 20 20 20 20 20 20 20 | 11 32 32 20 20 20 20 20 |        |.22     |
|00002ab0| 20 20 20 20 20 32 20 20 | 20 20 32 20 20 20 20 20 |     2  |  2     |
|00002ac0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 32 20 |        |      2 |
|00002ad0| 20 20 20 20 20 20 20 20 | 20 32 20 20 20 20 20 20 |        | 2      |
|00002ae0| 32 0d 0b 00 20 20 20 20 | 20 11 31 28 11 33 78 20 |2...    | .1(.3x |
|00002af0| 11 31 2d 20 11 33 68 11 | 31 29 20 20 2b 20 28 11 |.1- .3h.|1)  + (.|
|00002b00| 33 79 20 11 31 2d 20 11 | 33 6b 11 31 29 20 20 3d |3y .1- .|3k.1)  =|
|00002b10| 20 11 33 72 20 20 20 20 | 11 34 35 35 36 20 20 20 | .3r    |.4556   |
|00002b20| 11 31 5b 11 33 78 20 11 | 31 2d 20 28 2d 33 29 5d |.1[.3x .|1- (-3)]|
|00002b30| 20 20 2b 20 28 11 33 79 | 20 11 31 2d 20 34 29 20 |  + (.3y| .1- 4) |
|00002b40| 20 3d 20 28 35 29 0d 0a | 00 20 20 20 20 20 20 20 | = (5)..|.       |
|00002b50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002b60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002b70| 20 20 20 20 20 20 20 20 | 20 11 32 32 20 20 20 20 |        | .22    |
|00002b80| 20 20 20 20 20 20 32 0d | 0b 00 20 20 20 20 20 20 |      2.|..      |
|00002b90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002ba0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002bb0| 20 20 20 11 31 28 11 33 | 78 20 11 31 2b 20 33 29 |   .1(.3|x .1+ 3)|
|00002bc0| 20 20 2b 20 28 11 33 79 | 20 11 31 2d 20 34 29 20 |  + (.3y| .1- 4) |
|00002bd0| 20 3d 20 32 35 0d 0a 00 | 00 17 4f 07 20 20 20 20 | = 25...|..O.    |
|00002be0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002bf0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002c00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002c10| 20 20 20 20 20 20 20 20 | 0d 0b 00 11 31 57 72 6f |        |....1Wro|
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|00002c30| 6e 74 65 72 20 28 11 33 | 68 11 31 2c 20 11 33 6b |nter (.3|h.1, .3k|
|00002c40| 11 31 29 20 3d 20 28 2d | 33 2c 20 34 29 20 61 6e |.1) = (-|3, 4) an|
|00002c50| 64 20 74 68 65 20 72 61 | 64 69 75 73 20 11 33 72 |d the ra|dius .3r|
|00002c60| 20 11 31 3d 20 35 2c 20 | 77 65 20 77 72 69 74 65 | .1= 5, |we write|
|00002c70| 20 0d 0a 00 74 68 65 20 | 73 74 61 6e 64 61 72 64 | ...the |standard|
|00002c80| 20 66 6f 72 6d 20 6f 66 | 20 74 68 65 20 65 71 75 | form of| the equ|
|00002c90| 61 74 69 6f 6e 20 6f 66 | 20 74 68 65 20 63 69 72 |ation of| the cir|
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|00002cb0| 30 0d 0a 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |0...    |        |
|00002cc0| 11 32 32 20 20 20 20 20 | 20 20 20 20 20 32 20 20 |.22     |     2  |
|00002cd0| 20 20 32 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |  2     |        |
|00002ce0| 20 20 20 20 20 20 32 20 | 20 20 20 20 20 20 20 20 |      2 |        |
|00002cf0| 20 32 20 20 20 20 20 20 | 32 0d 0b 00 20 20 20 20 | 2      |2...    |
|00002d00| 20 11 31 28 11 33 78 20 | 11 31 2d 20 11 33 68 11 | .1(.3x |.1- .3h.|
|00002d10| 31 29 20 20 2b 20 28 11 | 33 79 20 11 31 2d 20 11 |1)  + (.|3y .1- .|
|00002d20| 33 6b 11 31 29 20 20 3d | 20 11 33 72 20 20 20 20 |3k.1)  =| .3r    |
|00002d30| 11 34 35 35 36 20 20 20 | 11 31 5b 11 33 78 20 11 |.4556   |.1[.3x .|
|00002d40| 31 2d 20 28 2d 33 29 5d | 20 20 2b 20 28 11 33 79 |1- (-3)]|  + (.3y|
|00002d50| 20 11 31 2d 20 34 29 20 | 20 3d 20 28 35 29 0d 0a | .1- 4) | = (5)..|
|00002d60| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00002d70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00002da0| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|00002db0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002dc0| 20 20 20 20 20 20 20 20 | 20 20 20 11 31 28 11 33 |        |   .1(.3|
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|00002de0| 20 11 31 2d 20 34 29 20 | 20 3d 20 32 35 0d 0a 00 | .1- 4) | = 25...|
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|00002e00| 20 20 54 68 69 73 20 69 | 73 20 74 68 65 20 73 74 |  This i|s the st|
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|00002e40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002e50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00002e60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00002f00| 6c 65 20 61 73 20 66 6f | 6c 6c 6f 77 73 2e 12 30 |le as fo|llows..0|
|00002f10| 0d 0a 00 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |...     |       .|
|00002f20| 32 32 20 20 20 20 20 20 | 20 20 20 20 32 20 20 20 |22      |    2   |
|00002f30| 20 32 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | 2      |        |
|00002f40| 20 20 20 20 20 32 20 20 | 20 20 20 20 20 20 20 20 |     2  |        |
|00002f50| 32 20 20 20 20 20 20 32 | 0d 0b 00 20 20 20 20 20 |2      2|...     |
|00002f60| 11 31 28 11 33 78 20 11 | 31 2d 20 11 33 68 11 31 |.1(.3x .|1- .3h.1|
|00002f70| 29 20 20 2b 20 28 11 33 | 79 20 11 31 2d 20 11 33 |)  + (.3|y .1- .3|
|00002f80| 6b 11 31 29 20 20 3d 20 | 11 33 72 20 20 20 20 11 |k.1)  = |.3r    .|
|00002f90| 34 35 35 36 20 20 20 11 | 31 5b 11 33 78 20 11 31 |4556   .|1[.3x .1|
|00002fa0| 2d 20 28 2d 33 29 5d 20 | 20 2b 20 28 11 33 79 20 |- (-3)] | + (.3y |
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|00002fc0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|00003000| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
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|00003020| 20 20 20 20 20 20 20 20 | 20 20 11 31 28 11 33 78 |        |  .1(.3x|
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|00003380| 69 73 65 20 31 30 0f 20 | 20 20 20 0e 78 31 2d 31 |ise 10. |   .x1-1|
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|00003450| 6c 6c 6f 77 69 6e 67 20 | 70 6f 69 6e 74 73 20 6c |llowing |points l|
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|00003470| 6f 66 20 74 68 65 20 65 | 71 75 61 74 69 6f 6e 0d |of the e|quation.|
|00003480| 0a 00 20 20 20 20 20 20 | 11 32 32 20 20 20 20 20 |..      |.22     |
|00003490| 32 0d 0b 00 20 20 20 20 | 20 11 33 78 20 79 20 11 |2...    | .3x y .|
|000034a0| 31 2d 20 11 33 78 20 20 | 11 31 2b 20 34 11 33 79 |1- .3x  |.1+ 4.3y|
|000034b0| 20 11 31 3d 20 30 2e 0d | 0a 00 0d 0b 00 20 20 20 | .1= 0..|.....   |
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|000034d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
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|000034f0| 0d 0b 00 20 20 20 20 20 | 20 20 20 21 20 20 20 11 |...     |   !   .|
|00003500| 31 34 11 34 21 20 20 20 | 20 20 20 20 20 20 20 20 |14.4!   |        |
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|00003540| 20 11 34 32 21 20 20 20 | 20 20 20 20 20 20 20 20 | .42!   |        |
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|00003560| 49 2e 20 11 34 21 11 31 | 36 2c 20 11 34 32 32 21 |I. .4!.1|6, .422!|
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|00003580| 31 35 11 34 21 20 20 20 | 20 20 20 20 20 20 20 20 |15.4!   |        |
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|000035d0| 20 20 20 20 20 20 20 20 | 20 39 20 20 20 20 20 30 |        | 9     0|
|000035e0| 0d 0a 00 0d 0a 00 20 20 | 20 20 20 11 31 0e 33 2d |......  |   .1.3-|
|000035f0| 32 2d 35 61 0e 28 61 29 | 0f 20 49 20 20 20 20 20 |2-5a.(a)|. I     |
|00003600| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003610| 20 20 20 20 20 20 20 0e | 33 2d 32 2d 35 62 0e 28 |       .|3-2-5b.(|
|00003620| 62 29 0f 20 49 49 0d 0a | 00 0d 0b 00 20 20 20 20 |b). II..|....    |
|00003630| 20 0e 33 2d 32 2d 35 63 | 0e 28 63 29 0f 20 49 20 | .3-2-5c|.(c). I |
|00003640| 61 6e 64 20 49 49 20 20 | 20 20 20 20 20 20 20 20 |and II  |        |
|00003650| 20 20 20 20 20 20 20 20 | 20 20 20 0e 33 2d 32 2d |        |   .3-2-|
|00003660| 35 64 0e 28 64 29 0f 20 | 4e 6f 6e 65 20 6f 66 20 |5d.(d). |None of |
|00003670| 74 68 65 73 65 0d 0a 00 | 0d 0a 00 59 6f 75 20 6d |these...|...You m|
|00003680| 61 79 20 77 61 6e 74 20 | 74 6f 20 72 65 76 69 65 |ay want |to revie|
|00003690| 77 20 10 31 2d 31 2d 32 | 0e 65 31 2d 31 2d 31 0e |w .1-1-2|.e1-1-1.|
|000036a0| 47 75 69 64 65 64 20 45 | 78 61 6d 70 6c 65 20 31 |Guided E|xample 1|
|000036b0| 2e 0f 0d 0a 00 53 65 63 | 74 69 6f 6e 20 31 2e 31 |.....Sec|tion 1.1|
|000036c0| 20 20 47 72 61 70 68 73 | 20 61 6e 64 20 47 72 61 |  Graphs| and Gra|
|000036d0| 70 68 69 6e 67 20 55 74 | 69 6c 69 74 69 65 73 20 |phing Ut|ilities |
|000036e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000036f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00003700| 20 20 20 20 20 20 20 20 | 20 20 11 32 33 0d 0b 00 |        |  .23...|
|00003710| 11 31 31 30 2e 20 20 53 | 6b 65 74 63 68 20 74 68 |.110.  S|ketch th|
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|000044d0| 79 11 31 2d 69 6e 74 65 | 72 63 65 70 74 3a 20 28 |y.1-inte|rcept: (|
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|000044f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 32 |        |       2|
|00004500| 0d 0a 00 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |......  |        |
|00004510| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004520| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004530| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004540| 20 33 0d 0b 00 20 20 20 | 20 20 0e 33 2d 32 2d 31 | 3...   |  .3-2-1|
|00004550| 39 63 0e 28 63 29 0f 20 | 11 33 78 11 31 2d 69 6e |9c.(c). |.3x.1-in|
|00004560| 74 65 72 63 65 70 74 3a | 20 28 2d 33 2c 20 30 29 |tercept:| (-3, 0)|
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|00004590| 2c 20 11 34 32 11 31 29 | 0d 0b 00 20 20 20 20 20 |, .42.1)|...     |
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|000045b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000045c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000045d0| 20 20 20 20 20 20 32 0d | 0a 00 0d 0b 00 20 20 20 |      2.|.....   |
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|00004600| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004610| 20 20 20 20 20 20 20 20 | 20 33 0d 0b 00 20 20 20 |        | 3...   |
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|00004640| 20 28 33 2c 20 30 29 20 | 20 20 20 20 20 20 20 20 | (3, 0) |        |
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|00004660| 63 65 70 74 3a 20 28 30 | 2c 20 2d 11 34 32 11 31 |cept: (0|, -.42.1|
|00004670| 29 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |)...    |        |
|00004680| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004690| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000046a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000046b0| 32 0d 0a 00 0d 0a 00 59 | 6f 75 20 6d 61 79 20 77 |2......Y|ou may w|
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|000046e0| 65 64 20 45 78 61 6d 70 | 6c 65 20 32 2e 0f 0d 0a |ed Examp|le 2....|
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|00004700| 61 70 68 73 20 61 6e 64 | 20 47 72 61 70 68 69 6e |aphs and| Graphin|
|00004710| 67 20 55 74 69 6c 69 74 | 69 65 73 0d 0b 00 20 34 |g Utilit|ies... 4|
|00004720| 2e 20 20 43 68 65 63 6b | 20 66 6f 72 20 73 79 6d |.  Check| for sym|
|00004730| 6d 65 74 72 79 20 77 69 | 74 68 20 72 65 73 70 65 |metry wi|th respe|
|00004740| 63 74 20 74 6f 20 62 6f | 74 68 20 61 78 65 73 20 |ct to bo|th axes |
|00004750| 61 6e 64 20 74 68 65 20 | 6f 72 69 67 69 6e 20 66 |and the |origin f|
|00004760| 6f 72 20 74 68 65 20 67 | 72 61 70 68 0d 0a 00 20 |or the g|raph... |
|00004770| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004780| 20 20 20 20 20 20 20 20 | 20 20 11 32 32 0d 0b 00 |        |  .22...|
|00004790| 20 20 20 20 20 11 31 6f | 66 20 74 68 65 20 65 71 |     .1o|f the eq|
|000047a0| 75 61 74 69 6f 6e 20 2d | 11 33 78 20 11 31 2b 20 |uation -|.3x .1+ |
|000047b0| 11 33 79 20 20 11 31 3d | 20 30 2e 0d 0a 00 0d 0a |.3y  .1=| 0......|
|000047c0| 00 20 20 20 20 20 0e 33 | 2d 32 2d 32 33 61 0e 28 |.     .3|-2-23a.(|
|000047d0| 61 29 0f 20 11 33 79 11 | 31 2d 61 78 69 73 20 73 |a). .3y.|1-axis s|
|000047e0| 79 6d 6d 65 74 72 79 20 | 20 20 20 20 20 20 20 20 |ymmetry |        |
|000047f0| 20 20 20 20 20 0e 33 2d | 32 2d 32 33 62 0e 28 62 |     .3-|2-23b.(b|
|00004800| 29 0f 20 11 33 78 11 31 | 2d 61 78 69 73 20 73 79 |). .3x.1|-axis sy|
|00004810| 6d 6d 65 74 72 79 0d 0a | 00 0d 0b 00 20 20 20 20 |mmetry..|....    |
|00004820| 20 0e 33 2d 32 2d 32 33 | 63 0e 28 63 29 0f 20 4f | .3-2-23|c.(c). O|
|00004830| 72 69 67 69 6e 20 73 79 | 6d 6d 65 74 72 79 20 20 |rigin sy|mmetry  |
|00004840| 20 20 20 20 20 20 20 20 | 20 20 20 20 0e 33 2d 32 |        |    .3-2|
|00004850| 2d 32 33 64 0e 28 64 29 | 0f 20 4e 6f 20 73 79 6d |-23d.(d)|. No sym|
|00004860| 6d 65 74 72 79 0d 0a 00 | 0d 0a 00 59 6f 75 20 6d |metry...|...You m|
|00004870| 61 79 20 77 61 6e 74 20 | 74 6f 20 72 65 76 69 65 |ay want |to revie|
|00004880| 77 20 10 31 2d 31 2d 32 | 0e 65 31 2d 31 2d 33 0e |w .1-1-2|.e1-1-3.|
|00004890| 47 75 69 64 65 64 20 45 | 78 61 6d 70 6c 65 20 33 |Guided E|xample 3|
|000048a0| 2e 0f 0d 0a 00 53 65 63 | 74 69 6f 6e 20 31 2e 31 |.....Sec|tion 1.1|
|000048b0| 20 20 47 72 61 70 68 73 | 20 61 6e 64 20 47 72 61 |  Graphs| and Gra|
|000048c0| 70 68 69 6e 67 20 55 74 | 69 6c 69 74 69 65 73 0d |phing Ut|ilities.|
|000048d0| 0b 00 20 35 2e 20 20 43 | 68 65 63 6b 20 66 6f 72 |.. 5.  C|heck for|
|000048e0| 20 73 79 6d 6d 65 74 72 | 79 20 77 69 74 68 20 72 | symmetr|y with r|
|000048f0| 65 73 70 65 63 74 20 74 | 6f 20 62 6f 74 68 20 61 |espect t|o both a|
|00004900| 78 65 73 20 61 6e 64 20 | 74 68 65 20 6f 72 69 67 |xes and |the orig|
|00004910| 69 6e 20 66 6f 72 20 74 | 68 65 20 67 72 61 70 68 |in for t|he graph|
|00004920| 0d 0a 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|00004930| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 32 32 |        |     .22|
|00004940| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |...     |        |
|00004950| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 33 78 20 |        |    .3x |
|00004960| 20 11 31 2d 20 33 0d 0b | 00 20 20 20 20 20 6f 66 | .1- 3..|.     of|
|00004970| 20 74 68 65 20 65 71 75 | 61 74 69 6f 6e 20 11 33 | the equ|ation .3|
|00004980| 79 20 11 31 3d 20 11 34 | 32 32 32 32 32 32 20 11 |y .1= .4|222222 .|
|00004990| 31 2e 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |1....   |        |
|000049a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000049b0| 32 11 33 78 0d 0a 00 0d | 0a 00 20 20 20 20 20 11 |2.3x....|..     .|
|000049c0| 31 0e 33 2d 32 2d 32 37 | 61 0e 28 61 29 0f 20 11 |1.3-2-27|a.(a). .|
|000049d0| 33 79 11 31 2d 61 78 69 | 73 20 73 79 6d 6d 65 74 |3y.1-axi|s symmet|
|000049e0| 72 79 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |ry      |        |
|000049f0| 0e 33 2d 32 2d 32 37 62 | 0e 28 62 29 0f 20 11 33 |.3-2-27b|.(b). .3|
|00004a00| 78 11 31 2d 61 78 69 73 | 20 73 79 6d 6d 65 74 72 |x.1-axis| symmetr|
|00004a10| 79 0d 0a 00 0d 0b 00 20 | 20 20 20 20 0e 33 2d 32 |y...... |    .3-2|
|00004a20| 2d 32 37 63 0e 28 63 29 | 0f 20 4f 72 69 67 69 6e |-27c.(c)|. Origin|
|00004a30| 20 73 79 6d 6d 65 74 72 | 79 20 20 20 20 20 20 20 | symmetr|y       |
|00004a40| 20 20 20 20 20 20 20 0e | 33 2d 32 2d 32 37 64 0e |       .|3-2-27d.|
|00004a50| 28 64 29 0f 20 4e 6f 20 | 73 79 6d 6d 65 74 72 79 |(d). No |symmetry|
|00004a60| 0d 0a 00 0d 0a 00 59 6f | 75 20 6d 61 79 20 77 61 |......Yo|u may wa|
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|00004a80| 31 2d 32 0e 65 31 2d 31 | 2d 33 0e 47 75 69 64 65 |1-2.e1-1|-3.Guide|
|00004a90| 64 20 45 78 61 6d 70 6c | 65 20 33 2e 0f 0d 0a 00 |d Exampl|e 3.....|
|00004aa0| 53 65 63 74 69 6f 6e 20 | 31 2e 31 20 20 47 72 61 |Section |1.1  Gra|
|00004ab0| 70 68 73 20 61 6e 64 20 | 47 72 61 70 68 69 6e 67 |phs and |Graphing|
|00004ac0| 20 55 74 69 6c 69 74 69 | 65 73 0d 0b 00 20 36 2e | Utiliti|es... 6.|
|00004ad0| 20 20 46 69 6e 64 20 74 | 68 65 20 73 74 61 6e 64 |  Find t|he stand|
|00004ae0| 61 72 64 20 66 6f 72 6d | 20 6f 66 20 74 68 65 20 |ard form| of the |
|00004af0| 65 71 75 61 74 69 6f 6e | 20 6f 66 20 74 68 65 20 |equation| of the |
|00004b00| 63 69 72 63 6c 65 20 77 | 69 74 68 20 63 65 6e 74 |circle w|ith cent|
|00004b10| 65 72 20 28 2d 33 2c 20 | 34 29 0d 0a 00 20 20 20 |er (-3, |4)...   |
|00004b20| 20 20 61 6e 64 20 73 6f | 6c 75 74 69 6f 6e 20 70 |  and so|lution p|
|00004b30| 6f 69 6e 74 20 28 30 2c | 20 30 29 2e 0d 0a 00 0d |oint (0,| 0).....|
|00004b40| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|00004b50| 20 20 11 32 32 20 20 20 | 20 20 20 20 20 20 20 32 |  .22   |       2|
|00004b60| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004b70| 20 20 20 20 20 32 20 20 | 20 20 20 20 20 20 20 20 |     2  |        |
|00004b80| 32 20 20 20 20 11 34 44 | 32 0d 0b 00 20 20 20 20 |2    .4D|2...    |
|00004b90| 20 11 31 0e 33 2d 32 2d | 36 33 61 0e 28 61 29 0f | .1.3-2-|63a.(a).|
|00004ba0| 20 28 11 33 78 20 11 31 | 2d 20 33 29 20 20 2b 20 | (.3x .1|- 3)  + |
|00004bb0| 28 11 33 79 20 11 31 2b | 20 34 29 20 20 3d 20 33 |(.3y .1+| 4)  = 3|
|00004bc0| 20 20 20 20 20 20 0e 33 | 2d 32 2d 36 33 62 0e 28 |      .3|-2-63b.(|
|00004bd0| 62 29 0f 20 28 11 33 78 | 20 11 31 2d 20 33 29 20 |b). (.3x| .1- 3) |
|00004be0| 20 2b 20 28 11 33 79 20 | 11 31 2d 20 34 29 20 20 | + (.3y |.1- 4)  |
|00004bf0| 3d 20 11 34 53 20 11 31 | 35 0d 0a 00 0d 0b 00 20 |= .4S .1|5...... |
|00004c00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 |        |       .|
|00004c10| 32 32 20 20 20 20 20 20 | 20 20 20 20 32 20 20 20 |22      |    2   |
|00004c20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004c30| 20 20 32 20 20 20 20 20 | 20 20 20 20 20 32 0d 0b |  2     |     2..|
|00004c40| 00 20 20 20 20 20 11 31 | 0e 33 2d 32 2d 36 33 63 |.     .1|.3-2-63c|
|00004c50| 0e 28 63 29 0f 20 28 11 | 33 78 20 11 31 2b 20 33 |.(c). (.|3x .1+ 3|
|00004c60| 29 20 20 2b 20 28 11 33 | 79 20 11 31 2d 20 34 29 |)  + (.3|y .1- 4)|
|00004c70| 20 20 3d 20 32 35 20 20 | 20 20 20 0e 33 2d 32 2d |  = 25  |   .3-2-|
|00004c80| 36 33 64 0e 28 64 29 0f | 20 28 11 33 78 20 11 31 |63d.(d).| (.3x .1|
|00004c90| 2b 20 33 29 20 20 2b 20 | 28 11 33 79 20 11 31 2b |+ 3)  + |(.3y .1+|
|00004ca0| 20 34 29 20 20 3d 20 35 | 0d 0a 00 0d 0a 00 59 6f | 4)  = 5|......Yo|
|00004cb0| 75 20 6d 61 79 20 77 61 | 6e 74 20 74 6f 20 72 65 |u may wa|nt to re|
|00004cc0| 76 69 65 77 20 10 31 2d | 31 2d 32 0e 65 31 2d 31 |view .1-|1-2.e1-1|
|00004cd0| 2d 34 0e 47 75 69 64 65 | 64 20 45 78 61 6d 70 6c |-4.Guide|d Exampl|
|00004ce0| 65 20 34 2e 0f 0d 0a 00 | 53 65 63 74 69 6f 6e 20 |e 4.....|Section |
|00004cf0| 31 2e 31 20 20 47 72 61 | 70 68 73 20 61 6e 64 20 |1.1  Gra|phs and |
|00004d00| 47 72 61 70 68 69 6e 67 | 20 55 74 69 6c 69 74 69 |Graphing| Utiliti|
|00004d10| 65 73 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |es      |        |
|00004d20| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004d30| 20 20 20 20 20 20 20 20 | 11 32 32 20 20 20 20 20 |        |.22     |
|00004d40| 20 32 0d 0b 00 20 11 31 | 37 2e 20 20 46 69 6e 64 | 2... .1|7.  Find|
|00004d50| 20 74 68 65 20 63 65 6e | 74 65 72 20 61 6e 64 20 | the cen|ter and |
|00004d60| 72 61 64 69 75 73 20 6f | 66 20 31 36 11 33 78 20 |radius o|f 16.3x |
|00004d70| 20 11 31 2b 20 31 36 11 | 33 79 20 20 11 31 2b 20 | .1+ 16.|3y  .1+ |
|00004d80| 31 36 11 33 78 20 11 31 | 2b 20 34 30 11 33 79 20 |16.3x .1|+ 40.3y |
|00004d90| 11 31 2d 20 37 20 3d 20 | 30 2c 20 61 6e 64 20 73 |.1- 7 = |0, and s|
|00004da0| 6b 65 74 63 68 0d 0a 00 | 20 20 20 20 20 74 68 65 |ketch...|     the|
|00004db0| 20 67 72 61 70 68 20 6f | 66 20 74 68 65 20 65 71 | graph o|f the eq|
|00004dc0| 75 61 74 69 6f 6e 2e 0d | 0a 00 0d 0a 00 20 20 20 |uation..|.....   |
|00004dd0| 20 20 0e 33 2d 32 2d 37 | 33 61 0e 28 61 29 0f 20 |  .3-2-7|3a.(a). |
|00004de0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004df0| 20 20 0e 33 2d 32 2d 37 | 33 62 0e 28 62 29 0f 20 |  .3-2-7|3b.(b). |
|00004e00| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004e10| 20 20 0e 33 2d 32 2d 37 | 33 63 0e 28 63 29 0f 0d |  .3-2-7|3c.(c)..|
|00004e20| 0a 00 14 6a 33 2d 32 2d | 37 33 61 2e 6d 14 39 14 |...j3-2-|73a.m.9.|
|00004e30| 37 14 32 30 14 37 14 20 | 20 14 6a 33 2d 32 2d 37 |7.20.7. | .j3-2-7|
|00004e40| 33 62 2e 6d 14 33 31 14 | 37 14 32 30 14 37 14 20 |3b.m.31.|7.20.7. |
|00004e50| 20 14 6a 33 2d 32 2d 37 | 33 63 2e 6d 14 35 33 14 | .j3-2-7|3c.m.53.|
|00004e60| 37 14 32 30 14 37 14 20 | 20 0d 0a 00 0d 0a 00 0d |7.20.7. | .......|
|00004e70| 0a 00 0d 0a 00 0d 0a 00 | 0d 0a 00 20 20 20 20 20 |........|...     |
|00004e80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 31 20 20 |        |     1  |
|00004e90| 20 35 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | 5      |        |
|00004ea0| 20 20 20 20 31 20 20 20 | 20 35 20 20 20 20 20 20 |    1   | 5      |
|00004eb0| 20 20 20 20 20 20 20 20 | 20 20 31 20 20 20 20 35 |        |  1    5|
|00004ec0| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 43 65 6e 74 |...     |    Cent|
|00004ed0| 65 72 3a 20 28 11 34 32 | 20 11 31 2c 20 11 34 32 |er: (.42| .1, .42|
|00004ee0| 11 31 29 20 20 20 20 20 | 20 20 43 65 6e 74 65 72 |.1)     |  Center|
|00004ef0| 3a 20 28 2d 11 34 32 20 | 11 31 2c 20 2d 11 34 32 |: (-.42 |.1, -.42|
|00004f00| 11 31 29 20 20 20 20 20 | 43 65 6e 74 65 72 3a 20 |.1)     |Center: |
|00004f10| 28 2d 11 34 32 20 11 31 | 2c 20 2d 11 34 32 11 31 |(-.42 .1|, -.42.1|
|00004f20| 29 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |)...    |        |
|00004f30| 20 20 20 20 20 20 32 20 | 20 20 34 20 20 20 20 20 |      2 |  4     |
|00004f40| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 32 20 20 |        |     2  |
|00004f50| 20 20 34 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |  4     |        |
|00004f60| 20 20 20 32 20 20 20 20 | 34 0d 0a 00 20 20 20 20 |   2    |4...    |
|00004f70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 39 20 20 |        |     9  |
|00004f80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004f90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00004fa0| 20 20 20 20 20 20 20 20 | 20 33 0d 0b 00 20 20 20 |        | 3...   |
|00004fb0| 20 20 20 20 20 20 52 61 | 64 69 75 73 3a 20 11 34 |      Ra|dius: .4|
|00004fc0| 32 20 20 20 20 20 20 20 | 20 20 20 20 20 20 11 31 |2       |      .1|
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|00004fe0| 20 20 20 20 20 20 52 61 | 64 69 75 73 3a 20 11 34 |      Ra|dius: .4|
|00004ff0| 32 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |2...    |        |
|00005000| 20 20 20 20 20 11 31 34 | 20 20 20 20 20 20 20 20 |     .14|        |
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|00005020| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00005030| 20 20 20 32 0d 0a 00 0d | 0a 00 20 20 20 20 20 0e |   2....|..     .|
|00005040| 33 2d 32 2d 37 33 64 0e | 28 64 29 0f 20 4e 6f 6e |3-2-73d.|(d). Non|
|00005050| 65 20 6f 66 20 74 68 65 | 73 65 0d 0a 00 0d 0a 00 |e of the|se......|
|00005060| 59 6f 75 20 6d 61 79 20 | 77 61 6e 74 20 74 6f 20 |You may |want to |
|00005070| 72 65 76 69 65 77 20 10 | 31 2d 31 2d 32 0e 65 31 |review .|1-1-2.e1|
|00005080| 2d 31 2d 35 0e 47 75 69 | 64 65 64 20 45 78 61 6d |-1-5.Gui|ded Exam|
|00005090| 70 6c 65 20 35 2e 0f 0d | 0a 00 53 65 63 74 69 6f |ple 5...|..Sectio|
|000050a0| 6e 20 31 2e 31 20 20 47 | 72 61 70 68 73 20 61 6e |n 1.1  G|raphs an|
|000050b0| 64 20 47 72 61 70 68 69 | 6e 67 20 55 74 69 6c 69 |d Graphi|ng Utili|
|000050c0| 74 69 65 73 0d 0b 00 20 | 38 2e 20 20 53 6b 65 74 |ties... |8.  Sket|
|000050d0| 63 68 20 74 68 65 20 67 | 72 61 70 68 20 6f 66 20 |ch the g|raph of |
|000050e0| 74 68 65 20 65 71 75 61 | 74 69 6f 6e 20 11 33 79 |the equa|tion .3y|
|000050f0| 20 11 31 3d 20 2d 33 11 | 33 78 20 11 31 2b 20 32 | .1= -3.|3x .1+ 2|
|00005100| 2e 20 20 49 64 65 6e 74 | 69 66 79 20 61 6e 79 20 |.  Ident|ify any |
|00005110| 69 6e 74 65 72 63 65 70 | 74 73 20 0d 0a 00 20 20 |intercep|ts ...  |
|00005120| 20 20 20 61 6e 64 20 74 | 65 73 74 20 66 6f 72 20 |   and t|est for |
|00005130| 73 79 6d 6d 65 74 72 79 | 2e 0d 0a 00 0d 0a 00 20 |symmetry|....... |
|00005140| 20 20 20 20 0e 33 2d 32 | 2d 33 39 61 0e 28 61 29 |    .3-2|-39a.(a)|
|00005150| 0f 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00005160| 20 20 20 20 0e 33 2d 32 | 2d 33 39 62 0e 28 62 29 |    .3-2|-39b.(b)|
|00005170| 0f 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|00005180| 20 20 20 20 0e 33 2d 32 | 2d 33 39 63 0e 28 63 29 |    .3-2|-39c.(c)|
|00005190| 0f 0d 0a 00 14 6a 33 2d | 32 2d 33 39 61 2e 6d 14 |.....j3-|2-39a.m.|
|000051a0| 39 14 37 14 32 30 14 37 | 14 20 20 14 6a 33 2d 32 |9.7.20.7|.  .j3-2|
|000051b0| 2d 33 39 62 2e 6d 14 33 | 31 14 37 14 32 30 14 37 |-39b.m.3|1.7.20.7|
|000051c0| 14 20 20 14 6a 33 2d 32 | 2d 33 39 63 2e 6d 14 35 |.  .j3-2|-39c.m.5|
|000051d0| 33 14 37 14 32 30 14 37 | 14 20 20 0d 0a 00 0d 0a |3.7.20.7|.  .....|
|000051e0| 00 0d 0a 00 0d 0a 00 0d | 0a 00 0d 0a 00 20 20 20 |........|.....   |
|000051f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00005200| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00005210| 20 20 20 20 20 20 20 20 | 20 20 20 20 32 0d 0b 00 |        |    2...|
|00005220| 20 20 20 20 20 20 20 20 | 20 49 6e 74 65 72 63 65 |        | Interce|
|00005230| 70 74 73 3a 20 28 30 2c | 20 32 29 20 20 20 20 49 |pts: (0,| 2)    I|
|00005240| 6e 74 65 72 63 65 70 74 | 73 3a 20 28 30 2c 20 11 |ntercept|s: (0, .|
|00005250| 34 32 11 31 29 20 20 20 | 20 49 6e 74 65 72 63 65 |42.1)   | Interce|
|00005260| 70 74 73 3a 20 28 30 2c | 20 32 29 0d 0b 00 20 20 |pts: (0,| 2)...  |
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|000053a0| 73 65 0d 0a 00 0d 0a 00 | 59 6f 75 20 6d 61 79 20 |se......|You may |
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|000053d0| 65 67 72 61 74 65 64 20 | 45 78 61 6d 70 6c 65 20 |egrated |Example |
|000053e0| 31 2e 0f 0d 0a 00 53 65 | 63 74 69 6f 6e 20 31 2e |1.....Se|ction 1.|
|000053f0| 31 20 20 47 72 61 70 68 | 73 20 61 6e 64 20 47 72 |1  Graph|s and Gr|
|00005400| 61 70 68 69 6e 67 20 55 | 74 69 6c 69 74 69 65 73 |aphing U|tilities|
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|00005440| 00 20 11 31 39 2e 20 20 | 53 6b 65 74 63 68 20 74 |. .19.  |Sketch t|
|00005450| 68 65 20 67 72 61 70 68 | 20 6f 66 20 74 68 65 20 |he graph| of the |
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|00005480| 31 2b 20 33 2e 20 20 49 | 64 65 6e 74 69 66 79 20 |1+ 3.  I|dentify |
|00005490| 61 6e 79 20 0d 0a 00 20 | 20 20 20 20 69 6e 74 65 |any ... |    inte|
|000054a0| 72 63 65 70 74 73 20 61 | 6e 64 20 74 65 73 74 20 |rcepts a|nd test |
|000054b0| 66 6f 72 20 73 79 6d 6d | 65 74 72 79 2e 0d 0a 00 |for symm|etry....|
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|00005570| 00 20 20 20 20 20 20 20 | 20 20 49 6e 74 65 72 63 |.       |  Interc|
|00005580| 65 70 74 73 3a 20 28 30 | 2c 20 33 29 20 20 20 20 |epts: (0|, 3)    |
|00005590| 49 6e 74 65 72 63 65 70 | 74 73 3a 20 28 30 2c 20 |Intercep|ts: (0, |
|000055a0| 33 29 20 20 20 20 49 6e | 74 65 72 63 65 70 74 73 |3)    In|tercepts|
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|00005610| 32 2d 34 33 64 0e 28 64 | 29 0f 20 4e 6f 6e 65 20 |2-43d.(d|). None |
|00005620| 6f 66 20 74 68 65 73 65 | 0d 0a 00 0d 0a 00 59 6f |of these|......Yo|
|00005630| 75 20 6d 61 79 20 77 61 | 6e 74 20 74 6f 20 72 65 |u may wa|nt to re|
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|00005d90| 31 2d 39 00             |                         |1-9.    |        |
+--------+-------------------------+-------------------------+--------+--------+