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| Unknown | 1996-07-25 | 12.3 KB |
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| Confidence | Program | Detection | Match Type | Support
|
|---|
| 1%
| dexvert
| Eclipse Tutorial (other/eclipseTutorial)
| ext
| Unsupported |
| 1%
| dexvert
| JuggleKrazy Tutorial (other/juggleKrazyTutorial)
| ext
| Unsupported |
| 100%
| file
| data
| default
| |
| 100%
| gt2
| Kopftext: 'TUTOR 06'
| default (weak)
|
|
hex view+--------+-------------------------+-------------------------+--------+--------+
|00000000| 54 55 54 4f 52 20 30 36 | d2 2f 00 00 78 01 00 00 |TUTOR 06|./..x...|
|00000010| 53 65 63 74 69 6f 6e 20 | 32 2e 31 20 20 4c 69 6e |Section |2.1 Lin|
|00000020| 65 73 20 69 6e 20 74 68 | 65 20 50 6c 61 6e 65 0d |es in th|e Plane.|
|00000030| 0a 00 0d 0b 00 0e 65 32 | 2d 31 2d 31 0e 47 75 69 |......e2|-1-1.Gui|
|00000040| 64 65 64 20 45 78 61 6d | 70 6c 65 20 20 31 0f 20 |ded Exam|ple 1. |
|00000050| 20 43 61 6c 63 75 6c 61 | 74 69 6e 67 20 74 68 65 | Calcula|ting the|
|00000060| 20 53 6c 6f 70 65 20 6f | 66 20 61 20 4c 69 6e 65 | Slope o|f a Line|
|00000070| 0d 0a 00 0e 65 32 2d 31 | 2d 32 0e 47 75 69 64 65 |....e2-1|-2.Guide|
|00000080| 64 20 45 78 61 6d 70 6c | 65 20 20 32 0f 20 20 46 |d Exampl|e 2. F|
|00000090| 69 6e 64 69 6e 67 20 74 | 68 65 20 53 6c 6f 70 65 |inding t|he Slope|
|000000a0| 20 6f 66 20 61 20 4c 69 | 6e 65 20 50 61 73 73 69 | of a Li|ne Passi|
|000000b0| 6e 67 20 54 68 72 6f 75 | 67 68 20 54 77 6f 20 50 |ng Throu|gh Two P|
|000000c0| 6f 69 6e 74 73 0d 0a 00 | 0e 65 32 2d 31 2d 33 0e |oints...|.e2-1-3.|
|000000d0| 47 75 69 64 65 64 20 45 | 78 61 6d 70 6c 65 20 20 |Guided E|xample |
|000000e0| 33 0f 20 20 55 73 69 6e | 67 20 74 68 65 20 50 6f |3. Usin|g the Po|
|000000f0| 69 6e 74 2d 53 6c 6f 70 | 65 20 46 6f 72 6d 20 6f |int-Slop|e Form o|
|00000100| 66 20 74 68 65 20 45 71 | 75 61 74 69 6f 6e 20 6f |f the Eq|uation o|
|00000110| 66 20 61 20 4c 69 6e 65 | 0d 0a 00 0e 65 32 2d 31 |f a Line|....e2-1|
|00000120| 2d 34 0e 47 75 69 64 65 | 64 20 45 78 61 6d 70 6c |-4.Guide|d Exampl|
|00000130| 65 20 20 34 0f 20 20 55 | 73 69 6e 67 20 74 68 65 |e 4. U|sing the|
|00000140| 20 49 6e 74 65 72 63 65 | 70 74 20 46 6f 72 6d 20 | Interce|pt Form |
|00000150| 6f 66 20 74 68 65 20 45 | 71 75 61 74 69 6f 6e 20 |of the E|quation |
|00000160| 6f 66 20 61 20 4c 69 6e | 65 0d 0a 00 0e 65 32 2d |of a Lin|e....e2-|
|00000170| 31 2d 35 0e 47 75 69 64 | 65 64 20 45 78 61 6d 70 |1-5.Guid|ed Examp|
|00000180| 6c 65 20 20 35 0f 20 20 | 44 65 74 65 72 6d 69 6e |le 5. |Determin|
|00000190| 69 6e 67 20 57 68 65 74 | 68 65 72 20 4c 69 6e 65 |ing Whet|her Line|
|000001a0| 73 20 61 72 65 20 50 61 | 72 61 6c 6c 65 6c 20 6f |s are Pa|rallel o|
|000001b0| 72 20 50 65 72 70 65 6e | 64 69 63 75 6c 61 72 0d |r Perpen|dicular.|
|000001c0| 0a 00 0e 65 32 2d 31 2d | 36 0e 47 75 69 64 65 64 |...e2-1-|6.Guided|
|000001d0| 20 45 78 61 6d 70 6c 65 | 20 20 36 0f 20 20 46 69 | Example| 6. Fi|
|000001e0| 6e 64 69 6e 67 20 50 61 | 72 61 6c 6c 65 6c 20 61 |nding Pa|rallel a|
|000001f0| 6e 64 20 50 65 72 70 65 | 6e 64 69 63 75 6c 61 72 |nd Perpe|ndicular|
|00000200| 20 4c 69 6e 65 73 0d 0a | 00 0e 65 32 2d 31 2d 37 | Lines..|..e2-1-7|
|00000210| 0e 47 75 69 64 65 64 20 | 45 78 61 6d 70 6c 65 20 |.Guided |Example |
|00000220| 20 37 0f 20 20 41 6e 20 | 41 70 70 6c 69 63 61 74 | 7. An |Applicat|
|00000230| 69 6f 6e 3a 20 53 61 6c | 61 72 79 20 61 6e 64 20 |ion: Sal|ary and |
|00000240| 43 6f 6d 6d 69 73 73 69 | 6f 6e 0d 0a 00 0e 69 32 |Commissi|on....i2|
|00000250| 2d 31 2d 31 0e 49 6e 74 | 65 67 72 61 74 65 64 20 |-1-1.Int|egrated |
|00000260| 45 78 61 6d 70 6c 65 20 | 20 31 0f 20 20 55 73 69 |Example | 1. Usi|
|00000270| 6e 67 20 61 20 50 6f 69 | 6e 74 20 61 6e 64 20 74 |ng a Poi|nt and t|
|00000280| 68 65 20 53 6c 6f 70 65 | 20 74 6f 20 46 69 6e 64 |he Slope| to Find|
|00000290| 20 4f 74 68 65 72 20 50 | 6f 69 6e 74 73 20 6f 6e | Other P|oints on|
|000002a0| 20 61 20 4c 69 6e 65 0d | 0a 00 0e 69 32 2d 31 2d | a Line.|...i2-1-|
|000002b0| 32 0e 49 6e 74 65 67 72 | 61 74 65 64 20 45 78 61 |2.Integr|ated Exa|
|000002c0| 6d 70 6c 65 20 20 32 0f | 20 20 55 73 69 6e 67 20 |mple 2.| Using |
|000002d0| 74 68 65 20 53 6c 6f 70 | 65 20 61 6e 64 20 11 33 |the Slop|e and .3|
|000002e0| 79 11 31 2d 49 6e 74 65 | 72 63 65 70 74 20 74 6f |y.1-Inte|rcept to|
|000002f0| 20 53 6b 65 74 63 68 20 | 61 20 4c 69 6e 65 0d 0a | Sketch |a Line..|
|00000300| 00 0e 69 32 2d 31 2d 33 | 0e 49 6e 74 65 67 72 61 |..i2-1-3|.Integra|
|00000310| 74 65 64 20 45 78 61 6d | 70 6c 65 20 20 33 0f 20 |ted Exam|ple 3. |
|00000320| 20 55 73 69 6e 67 20 74 | 68 65 20 53 6c 6f 70 65 | Using t|he Slope|
|00000330| 20 61 6e 64 20 11 33 79 | 11 31 2d 49 6e 74 65 72 | and .3y|.1-Inter|
|00000340| 63 65 70 74 20 74 6f 20 | 53 6b 65 74 63 68 20 61 |cept to |Sketch a|
|00000350| 20 4c 69 6e 65 0d 0a 00 | 0e 69 32 2d 31 2d 34 0e | Line...|.i2-1-4.|
|00000360| 49 6e 74 65 67 72 61 74 | 65 64 20 45 78 61 6d 70 |Integrat|ed Examp|
|00000370| 6c 65 20 20 34 0f 20 20 | 46 69 6e 64 69 6e 67 20 |le 4. |Finding |
|00000380| 61 6e 20 45 71 75 61 74 | 69 6f 6e 20 6f 66 20 61 |an Equat|ion of a|
|00000390| 20 4c 69 6e 65 20 50 61 | 73 73 69 6e 67 20 54 68 | Line Pa|ssing Th|
|000003a0| 72 6f 75 67 68 20 54 77 | 6f 20 50 6f 69 6e 74 73 |rough Tw|o Points|
|000003b0| 0d 0a 00 0e 69 32 2d 31 | 2d 35 0e 49 6e 74 65 67 |....i2-1|-5.Integ|
|000003c0| 72 61 74 65 64 20 45 78 | 61 6d 70 6c 65 20 20 35 |rated Ex|ample 5|
|000003d0| 0f 20 20 46 69 6e 64 69 | 6e 67 20 61 6e 20 45 71 |. Findi|ng an Eq|
|000003e0| 75 61 74 69 6f 6e 20 6f | 66 20 61 20 4c 69 6e 65 |uation o|f a Line|
|000003f0| 20 50 61 73 73 69 6e 67 | 20 54 68 72 6f 75 67 68 | Passing| Through|
|00000400| 20 54 77 6f 20 50 6f 69 | 6e 74 73 0d 0a 00 0e 69 | Two Poi|nts....i|
|00000410| 32 2d 31 2d 36 0e 49 6e | 74 65 67 72 61 74 65 64 |2-1-6.In|tegrated|
|00000420| 20 45 78 61 6d 70 6c 65 | 20 20 36 0f 20 20 53 6b | Example| 6. Sk|
|00000430| 65 74 63 68 69 6e 67 20 | 74 68 65 20 47 72 61 70 |etching |the Grap|
|00000440| 68 20 6f 66 20 61 20 4c | 69 6e 65 0d 0a 00 53 65 |h of a L|ine...Se|
|00000450| 63 74 69 6f 6e 20 32 2e | 31 20 20 4c 69 6e 65 73 |ction 2.|1 Lines|
|00000460| 20 69 6e 20 74 68 65 20 | 50 6c 61 6e 65 0d 0b 00 | in the |Plane...|
|00000470| 45 73 74 69 6d 61 74 65 | 20 74 68 65 20 73 6c 6f |Estimate| the slo|
|00000480| 70 65 20 6f 66 20 74 68 | 65 20 67 69 76 65 6e 20 |pe of th|e given |
|00000490| 6c 69 6e 65 20 66 72 6f | 6d 0d 0a 00 69 74 73 20 |line fro|m...its |
|000004a0| 67 72 61 70 68 2e 20 20 | 20 20 20 20 20 20 20 20 |graph. | |
|000004b0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|000004c0| 20 20 20 20 20 20 20 20 | 20 20 20 14 6b 33 2d 33 | | .k3-3|
|000004d0| 2d 31 61 2e 6d 14 34 35 | 14 30 14 34 30 14 31 31 |-1a.m.45|.0.40.11|
|000004e0| 14 0d 0a 00 0d 0a 00 13 | 12 31 53 4f 4c 55 54 49 |........|.1SOLUTI|
|000004f0| 4f 4e 12 30 0d 0a 00 0d | 0b 00 52 65 6d 65 6d 62 |ON.0....|..Rememb|
|00000500| 65 72 2c 20 74 68 65 20 | 73 6c 6f 70 65 20 6f 66 |er, the |slope of|
|00000510| 20 61 20 6e 6f 6e 76 65 | 72 74 69 63 61 6c 20 6c | a nonve|rtical l|
|00000520| 69 6e 65 20 69 73 0d 0a | 00 74 68 65 20 6e 75 6d |ine is..|.the num|
|00000530| 62 65 72 20 6f 66 20 75 | 6e 69 74 73 20 74 68 65 |ber of u|nits the|
|00000540| 20 6c 69 6e 65 20 72 69 | 73 65 73 20 6f 72 20 66 | line ri|ses or f|
|00000550| 61 6c 6c 73 0d 0a 00 76 | 65 72 74 69 63 61 6c 6c |alls...v|erticall|
|00000560| 79 20 66 6f 72 20 65 61 | 63 68 20 75 6e 69 74 20 |y for ea|ch unit |
|00000570| 63 68 61 6e 67 65 20 66 | 72 6f 6d 20 6c 65 66 74 |change f|rom left|
|00000580| 20 74 6f 20 0d 0a 00 72 | 69 67 68 74 2e 13 0d 0a | to ...r|ight....|
|00000590| 00 0d 0a 00 0d 0a 00 0d | 0b 00 49 6e 20 74 68 69 |........|..In thi|
|000005a0| 73 20 63 61 73 65 2c 20 | 74 68 65 20 6c 69 6e 65 |s case, |the line|
|000005b0| 20 72 69 73 65 73 20 66 | 6f 75 72 20 75 6e 69 74 | rises f|our unit|
|000005c0| 73 20 66 6f 72 20 65 61 | 63 68 20 75 6e 69 74 20 |s for ea|ch unit |
|000005d0| 6f 66 20 68 6f 72 69 7a | 6f 6e 74 61 6c 20 63 68 |of horiz|ontal ch|
|000005e0| 61 6e 67 65 20 0d 0a 00 | 66 72 6f 6d 20 6c 65 66 |ange ...|from lef|
|000005f0| 74 20 74 6f 20 72 69 67 | 68 74 20 28 73 65 65 20 |t to rig|ht (see |
|00000600| 74 68 65 20 67 72 61 70 | 68 29 2e 20 20 14 6b 33 |the grap|h). .k3|
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|00000620| 31 31 14 13 0d 0a 00 0d | 0b 00 54 68 65 72 65 66 |11......|..Theref|
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|000007b0| 74 68 65 20 6c 69 6e 65 | 20 70 61 73 73 69 6e 67 |the line| passing|
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|00000850| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
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|00000880| 11 32 32 20 20 20 20 31 | 20 20 11 31 13 0d 0a 00 |.22 1| .1....|
|00000890| 0d 0b 00 49 66 20 77 65 | 20 6c 65 74 20 28 11 33 |...If we| let (.3|
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|00000950| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 11 33 6d | | .3m|
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|00000970| 3d 20 11 34 32 32 20 11 | 31 3d 20 31 0d 0b 00 20 |= .422 .|1= 1... |
|00000980| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
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|00000aa0| 74 20 70 61 73 73 65 73 | 20 74 68 72 6f 75 67 68 |t passes| through|
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|00000ae0| 68 65 6e 20 73 6b 65 74 | 63 68 20 74 68 65 20 67 |hen sket|ch the g|
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|00000b10| 4f 4e 12 30 0d 0a 00 0d | 0b 00 55 73 69 6e 67 20 |ON.0....|..Using |
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|00000b50| 77 65 20 68 61 76 65 20 | 74 68 65 20 66 6f 6c 6c |we have |the foll|
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|00000b70| 20 11 33 79 20 11 31 2d | 20 11 33 79 20 20 11 31 | .3y .1-| .3y .1|
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|00000ba0| 20 20 11 32 12 31 50 6f | 69 6e 74 2d 73 6c 6f 70 | .2.1Po|int-slop|
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|00000be0| 20 20 20 20 11 31 31 0d | 0b 00 20 20 20 20 20 20 | .11.|.. |
|00000bf0| 11 33 79 20 11 31 2d 20 | 35 20 3d 20 2d 11 34 32 |.3y .1- |5 = -.42|
|00000c00| 11 31 28 11 33 78 20 11 | 31 2d 20 32 29 20 20 20 |.1(.3x .|1- 2) |
|00000c10| 20 20 20 20 20 20 20 20 | 11 32 12 31 53 75 62 73 | |.2.1Subs|
|00000c20| 74 69 74 75 74 65 20 6d | 3d 2d 31 2f 33 20 61 6e |titute m|=-1/3 an|
|00000c30| 64 20 28 78 20 2c 20 79 | 20 29 3d 28 32 2c 20 35 |d (x , y| )=(2, 5|
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|00000c50| 20 20 20 20 20 11 31 33 | 20 20 20 20 20 20 20 20 | .13| |
|00000c60| 20 20 20 20 20 20 20 20 | 20 20 11 32 12 31 20 20 | | .2.1 |
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|00000c80| 20 20 20 20 20 20 31 20 | 20 20 31 20 20 20 20 20 | 1 | 1 |
|00000c90| 20 20 20 12 30 13 0d 0a | 00 20 20 20 20 20 20 20 | .0...|. |
|00000ca0| 20 20 20 20 20 20 20 20 | 11 31 31 20 20 20 20 32 | |.11 2|
|00000cb0| 0d 0b 00 20 20 20 20 20 | 20 11 33 79 20 11 31 2d |... | .3y .1-|
|00000cc0| 20 35 20 3d 20 2d 11 34 | 32 11 33 78 20 11 31 2b | 5 = -.4|2.3x .1+|
|00000cd0| 20 11 34 32 0d 0b 00 20 | 20 20 20 20 20 20 20 20 | .42... | |
|00000ce0| 20 20 20 20 20 20 11 31 | 33 20 20 20 20 33 13 0d | .1|3 3..|
|00000cf0| 0a 00 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |.. | |
|00000d00| 20 31 20 20 20 20 31 37 | 0d 0b 00 20 20 20 20 20 | 1 17|... |
|00000d10| 20 20 20 20 20 11 33 79 | 20 11 31 3d 20 2d 11 34 | .3y| .1= -.4|
|00000d20| 32 11 33 78 20 11 31 2b | 20 11 34 32 32 20 20 20 |2.3x .1+| .422 |
|00000d30| 20 20 20 20 20 20 20 20 | 20 11 31 12 31 11 32 45 | | .1.1.2E|
|00000d40| 71 75 61 74 69 6f 6e 20 | 69 6e 20 73 6c 6f 70 65 |quation |in slope|
|00000d50| 2d 69 6e 74 65 72 63 65 | 70 74 20 66 6f 72 6d 11 |-interce|pt form.|
|00000d60| 31 12 30 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |1.0... | |
|00000d70| 20 20 20 20 20 33 20 20 | 20 20 20 33 20 20 20 20 | 3 | 3 |
|00000d80| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000d90| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00000da0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 13 0d | | ..|
|00000db0| 0a 00 0d 0b 00 46 72 6f | 6d 20 74 68 69 73 20 66 |.....Fro|m this f|
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|00001b10| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00001b20| 20 20 33 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | 3 | |
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|00002a30| 2e 31 20 20 4c 69 6e 65 | 73 20 69 6e 20 74 68 65 |.1 Line|s in the|
|00002a40| 20 50 6c 61 6e 65 0d 0b | 00 46 69 6e 64 20 74 68 | Plane..|.Find th|
|00002a50| 65 20 67 65 6e 65 72 61 | 6c 20 66 6f 72 6d 20 6f |e genera|l form o|
|00002a60| 66 20 74 68 65 20 65 71 | 75 61 74 69 6f 6e 20 6f |f the eq|uation o|
|00002a70| 66 20 74 68 65 20 6c 69 | 6e 65 20 74 68 61 74 20 |f the li|ne that |
|00002a80| 70 61 73 73 65 73 20 74 | 68 72 6f 75 67 68 20 74 |passes t|hrough t|
|00002a90| 68 65 0d 0a 00 70 6f 69 | 6e 74 73 20 28 2d 33 2c |he...poi|nts (-3,|
|00002aa0| 20 34 29 20 61 6e 64 20 | 28 31 36 2c 20 34 29 2e | 4) and |(16, 4).|
|00002ab0| 0d 0a 00 0d 0b 00 13 12 | 31 53 4f 4c 55 54 49 4f |........|1SOLUTIO|
|00002ac0| 4e 12 30 0d 0a 00 49 66 | 20 77 65 20 6c 65 74 20 |N.0...If| we let |
|00002ad0| 28 11 33 78 20 11 31 2c | 20 11 33 79 20 11 31 29 |(.3x .1,| .3y .1)|
|00002ae0| 20 3d 20 28 2d 33 2c 20 | 34 29 20 61 6e 64 20 28 | = (-3, |4) and (|
|00002af0| 11 33 78 20 11 31 2c 20 | 11 33 79 20 11 31 29 20 |.3x .1, |.3y .1) |
|00002b00| 3d 20 28 31 36 2c 20 34 | 29 2c 20 74 68 65 6e 20 |= (16, 4|), then |
|00002b10| 77 65 20 63 61 6e 20 61 | 70 70 6c 79 20 74 68 65 |we can a|pply the|
|00002b20| 20 0d 0b 00 20 20 20 20 | 20 20 20 20 20 20 20 20 | ... | |
|00002b30| 11 32 31 20 20 20 31 20 | 20 20 20 20 20 20 20 20 |.21 1 | |
|00002b40| 20 20 20 20 20 20 20 20 | 20 32 20 20 20 32 0d 0a | | 2 2..|
|00002b50| 00 11 31 66 6f 72 6d 75 | 6c 61 20 66 6f 72 20 74 |..1formu|la for t|
|00002b60| 68 65 20 73 6c 6f 70 65 | 20 6f 66 20 61 20 6c 69 |he slope| of a li|
|00002b70| 6e 65 20 61 73 20 66 6f | 6c 6c 6f 77 73 2e 0d 0a |ne as fo|llows...|
|00002b80| 00 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |. | |
|00002b90| 20 20 20 20 20 20 20 20 | 11 33 79 20 20 11 31 2d | |.3y .1-|
|00002ba0| 20 11 33 79 0d 0b 00 20 | 20 20 20 20 20 20 20 20 | .3y... | |
|00002bb0| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 11 | | .|
|00002bc0| 32 32 20 20 20 20 31 20 | 20 20 20 20 11 31 34 20 |22 1 | .14 |
|00002bd0| 2d 20 34 0d 0b 00 20 20 | 20 20 20 20 20 20 20 20 |- 4... | |
|00002be0| 20 20 20 20 20 20 20 20 | 20 11 33 6d 20 11 31 3d | | .3m .1=|
|00002bf0| 20 11 34 32 32 32 32 32 | 32 32 20 11 31 3d 20 11 | .422222|22 .1= .|
|00002c00| 34 32 32 32 32 32 32 32 | 32 32 20 11 31 3d 20 30 |42222222|22 .1= 0|
|00002c10| 0d 0b 00 20 20 20 20 20 | 20 20 20 20 20 20 20 20 |... | |
|00002c20| 20 20 20 20 20 20 20 20 | 20 20 11 33 78 20 20 11 | | .3x .|
|00002c30| 31 2d 20 11 33 78 20 20 | 20 20 11 31 31 36 20 2d |1- .3x | .116 -|
|00002c40| 20 28 2d 33 29 0d 0b 00 | 20 20 20 20 20 20 20 20 | (-3)...| |
|00002c50| 20 20 20 20 20 20 20 20 | 20 20 20 20 20 20 20 20 | | |
|00002c60| 11 32 32 20 20 20 20 31 | 20 20 20 20 20 20 20 20 |.22 1| |
|00002c70| 20 20 20 20 20 20 20 20 | 20 20 11 31 13 0d 0a 00 | | .1....|
|00002c80| 42 65 63 61 75 73 65 20 | 74 68 65 20 73 6c 6f 70 |Because |the slop|
|00002c90| 65 20 69 73 20 7a 65 72 | 6f 2c 20 77 65 20 6b 6e |e is zer|o, we kn|
|00002ca0| 6f 77 20 74 68 61 74 20 | 74 68 65 20 6c 69 6e 65 |ow that |the line|
|00002cb0| 20 69 73 20 68 6f 72 69 | 7a 6f 6e 74 61 6c 2e 13 | is hori|zontal..|
|00002cc0| 0d 0a 00 0d 0b 00 46 72 | 6f 6d 20 74 68 65 20 70 |......Fr|om the p|
|00002cd0| 6f 69 6e 74 73 20 77 65 | 20 73 65 65 20 74 68 61 |oints we| see tha|
|00002ce0| 74 20 74 68 65 20 11 33 | 79 11 31 2d 63 6f 6f 72 |t the .3|y.1-coor|
|00002cf0| 64 69 6e 61 74 65 20 6f | 66 20 65 61 63 68 20 70 |dinate o|f each p|
|00002d00| 6f 69 6e 74 20 6f 6e 20 | 74 68 65 20 6c 69 6e 65 |oint on |the line|
|00002d10| 20 69 73 20 34 2e 13 0d | 0a 00 0d 0b 00 54 68 65 | is 4...|.....The|
|00002d20| 72 65 66 6f 72 65 2c 20 | 74 68 65 20 65 71 75 61 |refore, |the equa|
|00002d30| 74 69 6f 6e 20 6f 66 20 | 74 68 65 20 6c 69 6e 65 |tion of |the line|
|00002d40| 20 69 73 0d 0a 00 0d 0b | 00 20 20 20 20 20 20 20 | is.....|. |
|00002d50| 20 20 20 11 33 79 20 11 | 31 3d 20 34 20 20 20 20 | .3y .|1= 4 |
|00002d60| 20 6f 72 20 69 6e 20 67 | 65 6e 65 72 61 6c 20 66 | or in g|eneral f|
|00002d70| 6f 72 6d 20 20 20 20 20 | 11 33 79 20 11 31 2d 20 |orm |.3y .1- |
|00002d80| 34 20 3d 20 30 2e 0d 0a | 00 53 65 63 74 69 6f 6e |4 = 0...|.Section|
|00002d90| 20 32 2e 31 20 20 4c 69 | 6e 65 73 20 69 6e 20 74 | 2.1 Li|nes in t|
|00002da0| 68 65 20 50 6c 61 6e 65 | 0d 0b 00 46 69 6e 64 20 |he Plane|...Find |
|00002db0| 61 6e 20 65 71 75 61 74 | 69 6f 6e 20 6f 66 20 74 |an equat|ion of t|
|00002dc0| 68 65 20 6c 69 6e 65 20 | 74 68 61 74 20 70 61 73 |he line |that pas|
|00002dd0| 73 65 73 20 74 68 72 6f | 75 67 68 20 74 68 65 20 |ses thro|ugh the |
|00002de0| 70 6f 69 6e 74 20 28 30 | 2c 20 33 29 20 61 6e 64 |point (0|, 3) and|
|00002df0| 20 68 61 73 20 61 6e 0d | 0a 00 75 6e 64 65 66 69 | has an.|..undefi|
|00002e00| 6e 65 64 20 73 6c 6f 70 | 65 2e 0d 0a 00 0d 0b 00 |ned slop|e.......|
|00002e10| 13 12 31 53 4f 4c 55 54 | 49 4f 4e 12 30 0d 0a 00 |..1SOLUT|ION.0...|
|00002e20| 42 65 63 61 75 73 65 20 | 74 68 65 20 73 6c 6f 70 |Because |the slop|
|00002e30| 65 20 69 73 20 75 6e 64 | 65 66 69 6e 65 64 2c 20 |e is und|efined, |
|00002e40| 77 65 20 6b 6e 6f 77 20 | 74 68 61 74 20 74 68 65 |we know |that the|
|00002e50| 20 6c 69 6e 65 20 69 73 | 20 76 65 72 74 69 63 61 | line is| vertica|
|00002e60| 6c 2e 13 0d 0a 00 0d 0b | 00 54 68 69 73 20 69 6e |l.......|.This in|
|00002e70| 64 69 63 61 74 65 73 20 | 74 68 61 74 20 74 68 65 |dicates |that the|
|00002e80| 20 11 33 78 11 31 2d 63 | 6f 6f 72 64 69 6e 61 74 | .3x.1-c|oordinat|
|00002e90| 65 20 6f 66 20 65 76 65 | 72 79 20 70 6f 69 6e 74 |e of eve|ry point|
|00002ea0| 20 6f 6e 20 74 68 65 20 | 6c 69 6e 65 20 69 73 20 | on the |line is |
|00002eb0| 74 68 65 20 73 61 6d 65 | 2e 13 0d 0a 00 0d 0b 00 |the same|........|
|00002ec0| 54 68 65 72 65 66 6f 72 | 65 2c 20 74 68 65 20 65 |Therefor|e, the e|
|00002ed0| 71 75 61 74 69 6f 6e 20 | 6f 66 20 74 68 65 20 6c |quation |of the l|
|00002ee0| 69 6e 65 20 69 73 20 11 | 33 78 20 11 31 3d 20 30 |ine is .|3x .1= 0|
|00002ef0| 2e 13 0d 0a 00 0d 0b 00 | 57 68 65 6e 20 77 65 20 |........|When we |
|00002f00| 73 6b 65 74 63 68 20 74 | 68 65 20 67 72 61 70 68 |sketch t|he graph|
|00002f10| 20 6f 66 20 61 20 76 65 | 72 74 69 63 61 6c 20 6c | of a ve|rtical l|
|00002f20| 69 6e 65 0d 0a 00 74 68 | 61 74 20 70 61 73 73 65 |ine...th|at passe|
|00002f30| 73 20 74 68 72 6f 75 67 | 68 20 74 68 65 20 70 6f |s throug|h the po|
|00002f40| 69 6e 74 20 28 30 2c 20 | 33 29 2c 20 77 65 20 73 |int (0, |3), we s|
|00002f50| 65 65 0d 0a 00 74 68 61 | 74 20 74 68 65 20 67 72 |ee...tha|t the gr|
|00002f60| 61 70 68 20 63 6f 69 6e | 63 69 64 65 73 20 77 69 |aph coin|cides wi|
|00002f70| 74 68 20 74 68 65 20 11 | 33 79 11 31 2d 61 78 69 |th the .|3y.1-axi|
|00002f80| 73 20 61 73 0d 0a 00 73 | 68 6f 77 6e 20 69 6e 20 |s as...s|hown in |
|00002f90| 74 68 65 20 66 69 67 75 | 72 65 20 61 74 20 74 68 |the figu|re at th|
|00002fa0| 65 20 72 69 67 68 74 2e | 20 20 20 20 20 20 20 20 |e right.| |
|00002fb0| 20 20 20 20 20 20 20 20 | 20 14 6b 33 2d 33 2d 31 | | .k3-3-1|
|00002fc0| 30 2e 6d 14 35 32 14 31 | 38 14 34 30 14 38 14 0d |0.m.52.1|8.40.8..|
|00002fd0| 0a 00 2f 00 00 00 1f 04 | 00 00 4d 1f 00 00 10 00 |../.....|..M.....|
|00002fe0| 00 00 00 00 00 00 65 32 | 2d 31 00 6d 04 00 00 f9 |......e2|-1.m....|
|00002ff0| 01 00 00 4d 1f 00 00 4e | 04 00 00 00 00 00 00 65 |...M...N|.......e|
|00003000| 32 2d 31 2d 31 00 85 06 | 00 00 d9 03 00 00 4d 1f |2-1-1...|......M.|
|00003010| 00 00 66 06 00 00 00 00 | 00 00 65 32 2d 31 2d 32 |..f.....|..e2-1-2|
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|00003030| 00 00 00 00 00 65 32 2d | 31 2d 33 00 c2 0e 00 00 |.....e2-|1-3.....|
|00003040| 63 02 00 00 4d 1f 00 00 | a3 0e 00 00 00 00 00 00 |c...M...|........|
|00003050| 65 32 2d 31 2d 34 00 44 | 11 00 00 cd 03 00 00 4d |e2-1-4.D|.......M|
|00003060| 1f 00 00 25 11 00 00 00 | 00 00 00 65 32 2d 31 2d |...%....|...e2-1-|
|00003070| 35 00 30 15 00 00 a9 06 | 00 00 4d 1f 00 00 11 15 |5.0.....|..M.....|
|00003080| 00 00 00 00 00 00 65 32 | 2d 31 2d 36 00 f8 1b 00 |......e2|-1-6....|
|00003090| 00 bc 01 00 00 4d 1f 00 | 00 d9 1b 00 00 00 00 00 |.....M..|........|
|000030a0| 00 65 32 2d 31 2d 37 00 | d3 1d 00 00 cd 01 00 00 |.e2-1-7.|........|
|000030b0| 4d 1f 00 00 b4 1d 00 00 | 00 00 00 00 69 32 2d 31 |M.......|....i2-1|
|000030c0| 2d 31 00 bf 1f 00 00 d2 | 02 00 00 4d 1f 00 00 a0 |-1......|...M....|
|000030d0| 1f 00 00 00 00 00 00 69 | 32 2d 31 2d 32 00 b0 22 |.......i|2-1-2.."|
|000030e0| 00 00 3b 04 00 00 4d 1f | 00 00 91 22 00 00 00 00 |..;...M.|..."....|
|000030f0| 00 00 69 32 2d 31 2d 33 | 00 0a 27 00 00 1d 03 00 |..i2-1-3|..'.....|
|00003100| 00 4d 1f 00 00 eb 26 00 | 00 00 00 00 00 69 32 2d |.M....&.|.....i2-|
|00003110| 31 2d 34 00 46 2a 00 00 | 43 03 00 00 4d 1f 00 00 |1-4.F*..|C...M...|
|00003120| 27 2a 00 00 00 00 00 00 | 69 32 2d 31 2d 35 00 a8 |'*......|i2-1-5..|
|00003130| 2d 00 00 2a 02 00 00 4d | 1f 00 00 89 2d 00 00 00 |-..*...M|....-...|
|00003140| 00 00 00 69 32 2d 31 2d | 36 00 |...i2-1-|6. |
+--------+-------------------------+-------------------------+--------+--------+
