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|00000df0| 20 6c 69 6e 65 2c 20 77 | 65 20 66 69 6e 64 20 74 | line, w|e find t|
|00000e00| 68 65 20 65 71 75 61 74 | 69 6f 6e 20 61 73 20 66 |he equat|ion as f|
|00000e10| 6f 6c 6c 6f 77 73 2e 12 | 30 0d 0a 00 20 20 20 11 |ollows..|0...   .|
|00000e20| 33 79 20 11 31 2d 20 36 | 20 3d 20 2d 32 5b 11 33 |3y .1- 6| = -2[.3|
|00000e30| 78 20 11 31 2d 20 28 2d | 33 29 5d 20 20 20 11 34 |x .1- (-|3)]   .4|
|00000e40| 35 35 36 20 20 20 11 33 | 79 20 11 31 2d 20 36 20 |556   .3|y .1- 6 |
|00000e50| 3d 20 2d 32 28 11 33 78 | 20 11 31 2b 20 33 29 20 |= -2(.3x| .1+ 3) |
|00000e60| 20 20 0d 0a 00 20 20 20 | 20 20 20 20 20 20 20 20 |  ...   |        |
|00000e70| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00000e80| 20 20 20 20 20 11 33 79 | 20 11 31 2d 20 36 20 3d |     .3y| .1- 6 =|
|00000e90| 20 2d 32 11 33 78 20 11 | 31 2d 20 36 20 20 20 11 | -2.3x .|1- 6   .|
|00000ea0| 34 35 35 36 20 20 20 11 | 31 32 11 33 78 20 11 31 |4556   .|12.3x .1|
|00000eb0| 2b 20 11 33 79 20 11 31 | 3d 20 30 0d 0a 00 55 73 |+ .3y .1|= 0...Us|
|00000ec0| 65 20 74 68 65 20 66 69 | 6e 61 6c 20 65 71 75 61 |e the fi|nal equa|
|00000ed0| 74 69 6f 6e 20 74 6f 20 | 73 6b 65 74 63 68 20 74 |tion to |sketch t|
|00000ee0| 68 65 20 6c 69 6e 65 2e | 0d 0a 00 00 17 4f 03 0d |he line.|.....O..|
|00000ef0| 0b 00 57 72 6f 6e 67 2e | 20 20 41 20 68 6f 72 69 |..Wrong.|  A hori|
|00000f00| 7a 6f 6e 74 61 6c 20 6c | 69 6e 65 20 68 61 73 20 |zontal l|ine has |
|00000f10| 61 20 64 65 66 69 6e 65 | 64 20 73 6c 6f 70 65 20 |a define|d slope |
|00000f20| 11 33 6d 20 11 31 3d 20 | 30 2e 20 20 54 72 79 20 |.3m .1= |0.  Try |
|00000f30| 61 67 61 69 6e 2e 0d 0a | 00 00 17 4f 05 0d 0b 00 |again...|...O....|
|00000f40| 57 72 6f 6e 67 2e 20 20 | 57 69 74 68 20 11 33 61 |Wrong.  |With .3a|
|00000f50| 20 11 31 3d 20 2d 35 2f | 36 20 61 6e 64 20 11 33 | .1= -5/|6 and .3|
|00000f60| 62 20 11 31 3d 20 2d 37 | 2f 33 2c 20 77 65 20 75 |b .1= -7|/3, we u|
|00000f70| 73 65 20 74 68 65 20 67 | 69 76 65 6e 20 66 6f 72 |se the g|iven for|
|00000f80| 6d 75 6c 61 20 61 73 20 | 66 6f 6c 6c 6f 77 73 2e |mula as |follows.|
|00000f90| 12 30 0d 0a 00 20 20 20 | 20 20 20 20 11 33 78 20 |.0...   |    .3x |
|00000fa0| 20 20 20 20 20 20 20 79 | 20 20 20 20 20 20 20 20 |       y|        |
|00000fb0| 20 20 20 20 20 20 20 20 | 11 31 36 20 20 20 20 33 |        |.16    3|
|00000fc0| 0d 0b 00 20 20 20 20 11 | 34 32 32 32 32 32 32 20 |...    .|4222222 |
|00000fd0| 11 31 2b 20 11 34 32 32 | 32 32 32 32 20 11 31 3d |.1+ .422|2222 .1=|
|00000fe0| 20 31 20 20 20 11 34 35 | 35 36 20 20 20 11 31 2d | 1   .45|56   .1-|
|00000ff0| 11 34 32 11 33 78 20 11 | 31 2d 20 11 34 32 11 33 |.42.3x .|1- .42.3|
|00001000| 79 20 11 31 2d 20 31 20 | 3d 20 30 20 20 20 11 34 |y .1- 1 |= 0   .4|
|00001010| 35 35 36 20 20 20 11 31 | 34 32 11 33 78 20 11 31 |556   .1|42.3x .1|
|00001020| 2b 20 31 35 11 33 79 20 | 11 31 2b 20 33 35 20 3d |+ 15.3y |.1+ 35 =|
|00001030| 20 30 0d 0b 00 20 20 20 | 20 28 2d 35 2f 36 29 20 | 0...   | (-5/6) |
|00001040| 20 20 28 2d 37 2f 33 29 | 20 20 20 20 20 20 20 20 |  (-7/3)|        |
|00001050| 20 20 20 20 20 20 35 20 | 20 20 20 37 0d 0a 00 00 |      5 |   7....|
|00001060| 17 4f 03 0d 0b 00 4e 6f | 74 20 71 75 69 74 65 2e |.O....No|t quite.|
|00001070| 20 20 43 68 65 63 6b 20 | 79 6f 75 72 20 63 61 6c |  Check |your cal|
|00001080| 63 75 6c 61 74 69 6f 6e | 73 2e 0d 0a 00 00 17 4f |culation|s......O|
|00001090| 04 0d 0b 00 57 72 6f 6e | 67 2e 20 20 54 68 69 73 |....Wron|g.  This|
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|000010b0| 6c 20 74 6f 20 74 68 65 | 20 67 69 76 65 6e 20 6c |l to the| given l|
|000010c0| 69 6e 65 2c 20 6e 6f 74 | 20 70 65 72 70 65 6e 64 |ine, not| perpend|
|000010d0| 69 63 75 6c 61 72 2e 20 | 20 54 72 79 20 0d 0a 00 |icular. | Try ...|
|000010e0| 61 67 61 69 6e 2e 0d 0a | 00 00 17 4f 03 0d 0b 00 |again...|...O....|
|000010f0| 52 69 67 68 74 2e 20 20 | 30 2e 30 33 11 33 53 20 |Right.  |0.03.3S |
|00001100| 11 31 3d 20 33 25 20 6f | 66 20 6d 6f 6e 74 68 6c |.1= 3% o|f monthl|
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|00001120| 2c 35 30 30 20 65 71 75 | 61 6c 73 20 74 68 65 20 |,500 equ|als the |
|00001130| 73 61 6c 61 72 79 20 11 | 33 57 11 31 2e 0d 0a 00 |salary .|3W.1....|
|00001140| 00 17 4f 06 0d 0b 00 20 | 20 20 20 20 20 20 20 20 |..O.... |        |
|00001150| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001160| 11 33 79 20 20 11 31 2d | 20 11 33 79 0d 0b 00 20 |.3y  .1-| .3y... |
|00001170| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001180| 20 20 20 20 20 20 20 20 | 20 11 32 32 20 20 20 20 |        | .22    |
|00001190| 31 20 20 20 11 31 36 20 | 2d 20 28 2d 32 29 20 20 |1   .16 |- (-2)  |
|000011a0| 20 36 20 2b 20 32 20 20 | 20 38 0d 0b 00 52 69 67 | 6 + 2  | 8...Rig|
|000011b0| 68 74 2e 20 20 54 68 65 | 20 73 6c 6f 70 65 20 69 |ht.  The| slope i|
|000011c0| 73 20 11 33 6d 20 11 31 | 3d 20 11 34 32 32 32 32 |s .3m .1|= .42222|
|000011d0| 32 32 32 20 11 31 3d 20 | 11 34 32 32 32 32 32 32 |222 .1= |.4222222|
|000011e0| 32 32 20 11 31 3d 20 11 | 34 32 32 32 32 32 20 11 |22 .1= .|422222 .|
|000011f0| 31 3d 20 11 34 32 20 11 | 31 3d 20 32 2e 0d 0b 00 |1= .42 .|1= 2....|
|00001200| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001210| 20 20 20 20 20 20 20 20 | 20 11 33 78 20 20 11 31 |        | .3x  .1|
|00001220| 2d 20 11 33 78 20 20 20 | 20 11 31 31 20 2d 20 28 |- .3x   | .11 - (|
|00001230| 2d 33 29 20 20 20 31 20 | 2b 20 33 20 20 20 34 0d |-3)   1 |+ 3   4.|
|00001240| 0b 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |..      |        |
|00001250| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 32 32 20 |        |    .22 |
|00001260| 20 20 20 31 0d 0a 00 00 | 17 4f 03 0d 0b 00 4e 6f |   1....|.O....No|
|00001270| 2e 20 20 54 68 65 20 70 | 6f 69 6e 74 73 20 69 6e |.  The p|oints in|
|00001280| 20 49 49 20 6c 69 65 20 | 6f 6e 20 74 68 65 20 73 | II lie |on the s|
|00001290| 70 65 63 69 66 69 65 64 | 20 6c 69 6e 65 2c 20 62 |pecified| line, b|
|000012a0| 75 74 20 74 68 65 20 70 | 6f 69 6e 74 73 20 69 6e |ut the p|oints in|
|000012b0| 20 49 20 64 6f 20 6e 6f | 74 2e 0d 0a 00 00 17 4f | I do no|t......O|
|000012c0| 05 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |....    |        |
|000012d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000012e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000012f0| 11 33 79 20 20 11 31 2d | 20 11 33 79 0d 0b 00 20 |.3y  .1-| .3y... |
|00001300| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001310| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001320| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 32 32 20 |        |    .22 |
|00001330| 20 20 20 31 0d 0b 00 11 | 31 57 72 6f 6e 67 2e 20 |   1....|1Wrong. |
|00001340| 20 52 65 6d 65 6d 62 65 | 72 3a 20 54 68 65 20 73 | Remembe|r: The s|
|00001350| 6c 6f 70 65 20 69 73 20 | 67 69 76 65 6e 20 62 79 |lope is |given by|
|00001360| 20 11 33 6d 20 11 31 3d | 20 11 34 32 32 32 32 32 | .3m .1=| .422222|
|00001370| 32 32 11 31 2e 20 20 54 | 72 79 20 61 67 61 69 6e |22.1.  T|ry again|
|00001380| 2e 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 |....    |        |
|00001390| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000013a0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000013b0| 11 33 78 20 20 11 31 2d | 20 11 33 78 0d 0b 00 20 |.3x  .1-| .3x... |
|000013c0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000013d0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000013e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 11 32 32 20 |        |    .22 |
|000013f0| 20 20 20 31 0d 0a 00 00 | 17 4f 05 0d 0b 00 52 69 |   1....|.O....Ri|
|00001400| 67 68 74 2e 20 20 54 68 | 65 73 65 20 6c 69 6e 65 |ght.  Th|ese line|
|00001410| 73 20 61 72 65 20 6e 6f | 74 20 70 61 72 61 6c 6c |s are no|t parall|
|00001420| 65 6c 20 62 65 63 61 75 | 73 65 20 74 68 65 69 72 |el becau|se their|
|00001430| 20 73 6c 6f 70 65 73 20 | 61 72 65 20 6e 6f 74 20 | slopes |are not |
|00001440| 65 71 75 61 6c 2e 0d 0a | 00 20 20 20 20 20 20 20 |equal...|.       |
|00001450| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001460| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001470| 31 0d 0b 00 28 53 6c 6f | 70 65 20 66 6f 72 20 11 |1...(Slo|pe for .|
|00001480| 33 4c 20 20 11 31 69 73 | 20 11 33 6d 20 11 31 3d |3L  .1is| .3m .1=|
|00001490| 20 2d 32 2c 20 66 6f 72 | 20 11 33 4c 20 20 11 31 | -2, for| .3L  .1|
|000014a0| 69 73 20 11 33 6d 20 11 | 31 3d 20 11 34 32 11 31 |is .3m .|1= .42.1|
|000014b0| 2e 29 0d 0b 00 20 20 20 | 20 20 20 20 20 20 20 20 |.)...   |        |
|000014c0| 20 11 32 31 20 20 20 20 | 20 20 20 20 20 20 20 20 | .21    |        |
|000014d0| 20 20 20 20 20 32 20 20 | 20 20 20 20 20 20 11 31 |     2  |      .1|
|000014e0| 32 0d 0a 00 00 17 4f 04 | 0d 0b 00 57 72 6f 6e 67 |2.....O.|...Wrong|
|000014f0| 2e 20 20 54 68 69 73 20 | 69 73 20 74 68 65 20 67 |.  This |is the g|
|00001500| 72 61 70 68 20 6f 66 20 | 11 33 79 20 11 31 2b 20 |raph of |.3y .1+ |
|00001510| 32 20 3d 20 30 2c 20 6e | 6f 74 20 11 33 79 20 11 |2 = 0, n|ot .3y .|
|00001520| 31 2d 20 32 20 3d 20 30 | 2e 20 20 0d 0a 00 00 17 |1- 2 = 0|.  .....|
|00001530| 4f 05 0d 0b 00 57 72 6f | 6e 67 2e 20 20 54 6f 20 |O....Wro|ng.  To |
|00001540| 73 6b 65 74 63 68 20 74 | 68 65 20 67 72 61 70 68 |sketch t|he graph|
|00001550| 2c 20 66 69 72 73 74 20 | 70 75 74 20 74 68 65 20 |, first |put the |
|00001560| 65 71 75 61 74 69 6f 6e | 20 69 6e 20 73 6c 6f 70 |equation| in slop|
|00001570| 65 2d 69 6e 74 65 72 63 | 65 70 74 20 0d 0a 00 0d |e-interc|ept ....|
|00001580| 0b 00 66 6f 72 6d 2e 20 | 20 49 74 20 61 70 70 65 |..form. | It appe|
|00001590| 61 72 73 20 74 68 61 74 | 20 79 6f 75 20 70 75 74 |ars that| you put|
|000015a0| 20 33 11 33 78 20 11 31 | 2b 20 32 11 33 79 20 11 | 3.3x .1|+ 2.3y .|
|000015b0| 31 2d 20 32 20 3d 20 30 | 20 69 6e 74 6f 20 73 6c |1- 2 = 0| into sl|
|000015c0| 6f 70 65 2d 69 6e 74 65 | 72 63 65 70 74 20 66 6f |ope-inte|rcept fo|
|000015d0| 72 6d 0d 0a 00 20 20 20 | 20 20 20 20 20 20 20 20 |rm...   |        |
|000015e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000015f0| 20 20 20 20 20 20 20 20 | 20 20 20 20 33 0d 0b 00 |        |    3...|
|00001600| 69 6e 63 6f 72 72 65 63 | 74 6c 79 2e 20 20 54 68 |incorrec|tly.  Th|
|00001610| 65 20 63 6f 72 72 65 63 | 74 20 66 6f 72 6d 20 69 |e correc|t form i|
|00001620| 73 20 11 33 79 20 11 31 | 3d 20 2d 11 34 32 11 33 |s .3y .1|= -.42.3|
|00001630| 78 20 11 31 2b 20 31 2e | 0d 0b 00 20 20 20 20 20 |x .1+ 1.|...     |
|00001640| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001650| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|00001660| 20 20 32 0d 0a 00 00 17 | 4f 03 0d 0b 00 57 72 6f |  2.....|O....Wro|
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|00001680| 63 61 6c 63 75 6c 61 74 | 69 6f 6e 73 2e 0d 0a 00 |calculat|ions....|
|00001690| 00 17 4f 04 0d 0b 00 57 | 72 6f 6e 67 2e 20 20 54 |..O....W|rong.  T|
|000016a0| 68 65 20 68 6f 72 69 7a | 6f 6e 74 61 6c 20 6c 69 |he horiz|ontal li|
|000016b0| 6e 65 20 11 33 79 20 11 | 31 2d 20 37 2e 35 20 3d |ne .3y .|1- 7.5 =|
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|000016d0| 20 74 68 72 6f 75 67 68 | 20 74 68 65 20 70 6f 69 | through| the poi|
|000016e0| 6e 74 73 20 0d 0a 00 28 | 37 2e 35 2c 20 32 29 20 |nts ...(|7.5, 2) |
|000016f0| 61 6e 64 20 28 37 2e 35 | 2c 20 39 29 2e 20 20 57 |and (7.5|, 9).  W|
|00001700| 65 20 77 61 6e 74 20 61 | 20 6c 69 6e 65 20 74 68 |e want a| line th|
|00001710| 61 74 20 70 61 73 73 65 | 73 20 74 68 72 6f 75 67 |at passe|s throug|
|00001720| 68 20 62 6f 74 68 20 70 | 6f 69 6e 74 73 2e 0d 0a |h both p|oints...|
|00001730| 00 00 17 4f 06 0d 0b 00 | 4e 6f 2e 20 20 55 73 69 |...O....|No.  Usi|
|00001740| 6e 67 20 74 68 65 20 70 | 6f 69 6e 74 2d 73 6c 6f |ng the p|oint-slo|
|00001750| 70 65 20 66 6f 72 6d 20 | 6f 66 20 61 20 6c 69 6e |pe form |of a lin|
|00001760| 65 2c 20 77 65 20 66 69 | 6e 64 20 74 68 65 20 65 |e, we fi|nd the e|
|00001770| 71 75 61 74 69 6f 6e 20 | 61 73 20 66 6f 6c 6c 6f |quation |as follo|
|00001780| 77 73 2e 12 30 0d 0a 00 | 20 20 20 11 33 79 20 11 |ws..0...|   .3y .|
|00001790| 31 2d 20 36 20 3d 20 2d | 32 5b 11 33 78 20 11 31 |1- 6 = -|2[.3x .1|
|000017a0| 2d 20 28 2d 33 29 5d 20 | 20 20 11 34 35 35 36 20 |- (-3)] |  .4556 |
|000017b0| 20 20 11 33 79 20 11 31 | 2d 20 36 20 3d 20 2d 32 |  .3y .1|- 6 = -2|
|000017c0| 28 11 33 78 20 11 31 2b | 20 33 29 20 20 20 0d 0a |(.3x .1+| 3)   ..|
|000017d0| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.       |        |
|000017e0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |        |        |
|000017f0| 20 11 33 79 20 11 31 2d | 20 36 20 3d 20 2d 32 11 | .3y .1-| 6 = -2.|
|00001800| 33 78 20 11 31 2d 20 36 | 20 20 20 11 34 35 35 36 |3x .1- 6|   .4556|
|00001810| 20 20 20 11 31 32 11 33 | 78 20 11 31 2b 20 11 33 |   .12.3|x .1+ .3|
|00001820| 79 20 11 31 3d 20 30 0d | 0a 00 55 73 65 20 74 68 |y .1= 0.|..Use th|
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|00001840| 20 74 6f 20 73 6b 65 74 | 63 68 20 74 68 65 20 6c | to sket|ch the l|
|00001850| 69 6e 65 2e 0d 0a 00 00 | 17 4f 03 0d 0b 00 52 69 |ine.....|.O....Ri|
|00001860| 67 68 74 2e 20 20 54 68 | 65 20 65 71 75 61 74 69 |ght.  Th|e equati|
|00001870| 6f 6e 20 6f 66 20 74 68 | 65 20 6c 69 6e 65 20 69 |on of th|e line i|
|00001880| 73 20 11 33 78 20 11 31 | 2d 20 36 20 3d 20 30 2e |s .3x .1|- 6 = 0.|
|00001890| 0d 0a 00 00 17 4f 05 0d | 0b 00 57 72 6f 6e 67 2e |.....O..|..Wrong.|
|000018a0| 20 20 57 69 74 68 20 11 | 33 61 20 11 31 3d 20 2d |  With .|3a .1= -|
|000018b0| 35 2f 36 20 61 6e 64 20 | 11 33 62 20 11 31 3d 20 |5/6 and |.3b .1= |
|000018c0| 2d 37 2f 33 2c 20 77 65 | 20 75 73 65 20 74 68 65 |-7/3, we| use the|
|000018d0| 20 67 69 76 65 6e 20 66 | 6f 72 6d 75 6c 61 20 61 | given f|ormula a|
|000018e0| 73 20 66 6f 6c 6c 6f 77 | 73 2e 12 30 0d 0a 00 20 |s follow|s..0... |
|000018f0| 20 20 20 20 20 20 11 33 | 78 20 20 20 20 20 20 20 |      .3|x       |
|00001900| 20 79 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | y      |        |
|00001910| 20 20 11 31 36 20 20 20 | 20 33 0d 0b 00 20 20 20 |  .16   | 3...   |
|00001920| 20 11 34 32 32 32 32 32 | 32 20 11 31 2b 20 11 34 | .422222|2 .1+ .4|
|00001930| 32 32 32 32 32 32 20 11 | 31 3d 20 31 20 20 20 11 |222222 .|1= 1   .|
|00001940| 34 35 35 36 20 20 20 11 | 31 2d 11 34 32 11 33 78 |4556   .|1-.42.3x|
|00001950| 20 11 31 2d 20 11 34 32 | 11 33 79 20 11 31 2d 20 | .1- .42|.3y .1- |
|00001960| 31 20 3d 20 30 20 20 20 | 11 34 35 35 36 20 20 20 |1 = 0   |.4556   |
|00001970| 11 31 34 32 11 33 78 20 | 11 31 2b 20 31 35 11 33 |.142.3x |.1+ 15.3|
|00001980| 79 20 11 31 2b 20 33 35 | 20 3d 20 30 0d 0b 00 20 |y .1+ 35| = 0... |
|00001990| 20 20 20 28 2d 35 2f 36 | 29 20 20 20 28 2d 37 2f |   (-5/6|)   (-7/|
|000019a0| 33 29 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |3)      |        |
|000019b0| 35 20 20 20 20 37 0d 0a | 00 00 17 4f 03 0d 0b 00 |5    7..|...O....|
|000019c0| 52 69 67 68 74 2e 20 20 | 54 68 69 73 20 6c 69 6e |Right.  |This lin|
|000019d0| 65 20 70 61 73 73 65 73 | 20 74 68 72 6f 75 67 68 |e passes| through|
|000019e0| 20 28 32 2c 20 31 29 20 | 61 6e 64 20 69 73 20 70 | (2, 1) |and is p|
|000019f0| 61 72 61 6c 6c 65 6c 20 | 74 6f 20 36 11 33 78 20 |arallel |to 6.3x |
|00001a00| 11 31 2d 20 32 11 33 79 | 20 11 31 3d 20 33 2e 0d |.1- 2.3y| .1= 3..|
|00001a10| 0a 00 00 17 4f 06 0d 0b | 00 57 72 6f 6e 67 2e 20 |....O...|.Wrong. |
|00001a20| 20 54 68 69 73 20 65 71 | 75 61 74 69 6f 6e 20 68 | This eq|uation h|
|00001a30| 61 73 20 74 68 65 20 73 | 61 6d 65 20 73 6c 6f 70 |as the s|ame slop|
|00001a40| 65 20 28 2d 35 2f 34 29 | 20 61 73 20 35 11 33 78 |e (-5/4)| as 5.3x|
|00001a50| 20 11 31 2b 20 34 11 33 | 79 20 11 31 3d 20 32 34 | .1+ 4.3|y .1= 24|
|00001a60| 2c 20 61 6e 64 20 0d 0a | 00 74 68 65 72 65 66 6f |, and ..|.therefo|
|00001a70| 72 65 20 69 73 20 70 61 | 72 61 6c 6c 65 6c 20 74 |re is pa|rallel t|
|00001a80| 6f 20 74 68 65 20 67 69 | 76 65 6e 20 6c 69 6e 65 |o the gi|ven line|
|00001a90| 2e 20 20 57 65 20 77 61 | 6e 74 20 74 6f 20 66 69 |.  We wa|nt to fi|
|00001aa0| 6e 64 20 61 20 6c 69 6e | 65 20 0d 0a 00 70 65 72 |nd a lin|e ...per|
|00001ab0| 70 65 6e 64 69 63 75 6c | 61 72 20 74 6f 20 74 68 |pendicul|ar to th|
|00001ac0| 65 20 67 69 76 65 6e 20 | 6c 69 6e 65 2e 20 20 41 |e given |line.  A|
|00001ad0| 6c 73 6f 2c 20 74 68 69 | 73 20 6c 69 6e 65 20 64 |lso, thi|s line d|
|00001ae0| 6f 65 73 20 6e 6f 74 20 | 70 61 73 73 20 74 68 72 |oes not |pass thr|
|00001af0| 6f 75 67 68 20 74 68 65 | 20 0d 0a 00 67 69 76 65 |ough the| ...give|
|00001b00| 6e 20 70 6f 69 6e 74 2e | 0d 0a 00 00 17 4f 03 0d |n point.|.....O..|
|00001b10| 0b 00 57 72 6f 6e 67 2e | 20 20 30 2e 33 53 20 11 |..Wrong.|  0.3S .|
|00001b20| 34 3d 20 11 31 33 25 20 | 6f 66 20 6d 6f 6e 74 68 |4= .13% |of month|
|00001b30| 6c 79 20 73 61 6c 65 73 | 2e 0d 0a 00 00 17 4f 04 |ly sales|......O.|
|00001b40| 0d 0b 00 57 72 6f 6e 67 | 2e 20 20 54 68 65 20 70 |...Wrong|.  The p|
|00001b50| 6f 69 6e 74 73 20 61 72 | 65 20 70 6c 6f 74 74 65 |oints ar|e plotte|
|00001b60| 64 20 63 6f 72 72 65 63 | 74 6c 79 2c 20 62 75 74 |d correc|tly, but|
|00001b70| 20 74 68 65 20 73 6c 6f | 70 65 20 6f 66 20 2d 32 | the slo|pe of -2|
|00001b80| 20 69 73 20 69 6e 63 6f | 72 72 65 63 74 2e 0d 0a | is inco|rrect...|
|00001b90| 00 43 68 65 63 6b 20 79 | 6f 75 72 20 63 61 6c 63 |.Check y|our calc|
|00001ba0| 75 6c 61 74 69 6f 6e 73 | 2e 0d 0a 00 00 17 4f 03 |ulations|......O.|
|00001bb0| 0d 0b 00 57 72 6f 6e 67 | 2e 20 20 54 68 65 20 70 |...Wrong|.  The p|
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|00001e80| 20 20 20 20 20 11 31 35 | 20 2d 20 28 2d 35 29 20 |     .15| - (-5) |
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|00002d10| 0e 28 64 29 0f 20 4e 6f | 20 6c 69 6e 65 2c 20 73 |.(d). No| line, s|
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|00003570| 20 11 34 32 20 11 31 2b | 20 11 34 32 20 11 31 3d | .42 .1+| .42 .1=|
|00003580| 20 31 2c 20 11 33 61 20 | 11 34 3d 20 11 31 30 2c | 1, .3a |.4= .10,|
|00003590| 20 11 33 62 20 11 34 3d | 20 11 31 30 2e 0d 0b 00 | .3b .4=| .10....|
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|00003600| 28 62 29 0f 20 36 11 33 | 78 20 11 31 2b 20 37 11 |(b). 6.3|x .1+ 7.|
|00003610| 33 79 20 11 31 2b 20 33 | 35 20 3d 20 30 0d 0a 00 |3y .1+ 3|5 = 0...|
|00003620| 0d 0b 00 20 20 20 20 20 | 0e 63 33 2d 33 2d 35 33 |...     |.c3-3-53|
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|00003900| 0a 00 20 20 20 20 20 20 | 20 20 20 11 33 4c 20 11 |..      |   .3L .|
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|00003950| 20 20 20 11 32 32 20 20 | 20 20 20 20 20 20 20 20 |   .22  |        |
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|00003970| 20 20 20 20 20 20 32 0d | 0a 00 0d 0a 00 11 31 59 |      2.|......1Y|
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|000039b0| 6c 65 20 35 2e 0f 0d 0a | 00 53 65 63 74 69 6f 6e |le 5....|.Section|
|000039c0| 20 32 2e 31 20 20 4c 69 | 6e 65 73 20 69 6e 20 74 | 2.1  Li|nes in t|
|000039d0| 68 65 20 50 6c 61 6e 65 | 0d 0b 00 20 36 2e 20 20 |he Plane|... 6.  |
|000039e0| 57 72 69 74 65 20 61 6e | 20 65 71 75 61 74 69 6f |Write an| equatio|
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|00003b10| 0d 0a 00 0d 0a 00 59 6f | 75 20 6d 61 79 20 77 61 |......Yo|u may wa|
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|00003b30| 31 2d 32 0e 65 32 2d 31 | 2d 36 0e 47 75 69 64 65 |1-2.e2-1|-6.Guide|
|00003b40| 64 20 45 78 61 6d 70 6c | 65 20 36 2e 0f 0d 0a 00 |d Exampl|e 6.....|
|00003b50| 53 65 63 74 69 6f 6e 20 | 32 2e 31 20 20 4c 69 6e |Section |2.1  Lin|
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|00003b70| 0b 00 20 37 2e 20 20 57 | 72 69 74 65 20 61 6e 20 |.. 7.  W|rite an |
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|00003bd0| 35 11 33 78 20 11 31 2b | 20 34 11 33 79 20 11 31 |5.3x .1+| 4.3y .1|
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|00003c70| 20 30 0d 0a 00 0d 0a 00 | 20 20 20 20 20 0e 63 33 | 0......|     .c3|
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|00003cd0| 20 30 0d 0a 00 0d 0a 00 | 59 6f 75 20 6d 61 79 20 | 0......|You may |
|00003ce0| 77 61 6e 74 20 74 6f 20 | 72 65 76 69 65 77 20 10 |want to |review .|
|00003cf0| 32 2d 31 2d 32 0e 65 32 | 2d 31 2d 36 0e 47 75 69 |2-1-2.e2|-1-6.Gui|
|00003d00| 64 65 64 20 45 78 61 6d | 70 6c 65 20 36 2e 0f 0d |ded Exam|ple 6...|
|00003d10| 0a 00 53 65 63 74 69 6f | 6e 20 32 2e 31 20 20 4c |..Sectio|n 2.1  L|
|00003d20| 69 6e 65 73 20 69 6e 20 | 74 68 65 20 50 6c 61 6e |ines in |the Plan|
|00003d30| 65 0d 0b 00 20 38 2e 20 | 20 41 20 73 61 6c 65 73 |e... 8. | A sales|
|00003d40| 20 72 65 70 72 65 73 65 | 6e 74 61 74 69 76 65 20 | represe|ntative |
|00003d50| 72 65 63 65 69 76 65 73 | 20 61 20 73 61 6c 61 72 |receives| a salar|
|00003d60| 79 20 6f 66 20 24 31 35 | 30 30 20 70 65 72 20 6d |y of $15|00 per m|
|00003d70| 6f 6e 74 68 20 70 6c 75 | 73 20 61 20 33 25 0d 0a |onth plu|s a 3%..|
|00003d80| 00 20 20 20 20 20 63 6f | 6d 6d 69 73 73 69 6f 6e |.     co|mmission|
|00003d90| 20 6f 66 20 74 6f 74 61 | 6c 20 6d 6f 6e 74 68 6c | of tota|l monthl|
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|00003db0| 61 20 6c 69 6e 65 61 72 | 20 65 71 75 61 74 69 6f |a linear| equatio|
|00003dc0| 6e 20 67 69 76 69 6e 67 | 20 74 68 65 0d 0a 00 20 |n giving| the... |
|00003dd0| 20 20 20 20 6d 6f 6e 74 | 68 6c 79 20 77 61 67 65 |    mont|hly wage|
|00003de0| 20 11 33 57 20 11 31 69 | 6e 20 74 65 72 6d 73 20 | .3W .1i|n terms |
|00003df0| 6f 66 20 6d 6f 6e 74 68 | 6c 79 20 73 61 6c 65 73 |of month|ly sales|
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|00003e30| 2b 20 31 35 30 30 20 20 | 20 20 20 20 20 20 20 20 |+ 1500  |        |
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|00003ed0| 20 11 31 2b 20 31 35 30 | 30 20 20 20 20 20 20 20 | .1+ 150|0       |
|00003ee0| 20 20 20 20 20 20 20 0e | 64 33 2d 33 2d 37 39 64 |       .|d3-3-79d|
|00003ef0| 0e 28 64 29 0f 20 11 33 | 57 20 11 31 3d 20 30 2e |.(d). .3|W .1= 0.|
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|00003f60| 73 20 69 6e 20 74 68 65 | 20 50 6c 61 6e 65 0d 0b |s in the| Plane..|
|00003f70| 00 20 39 2e 20 20 55 73 | 65 20 74 68 65 20 70 6f |. 9.  Us|e the po|
|00003f80| 69 6e 74 20 28 35 2c 20 | 32 29 20 61 6e 64 20 74 |int (5, |2) and t|
|00003f90| 68 65 20 73 6c 6f 70 65 | 20 6f 66 20 74 68 65 20 |he slope| of the |
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|00004900| 00                      |                         |.       |        |
+--------+-------------------------+-------------------------+--------+--------+