Download - Parallel and Perpendicular Lines
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Parallel and Perpendicular Lines
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Parallel Lines //All parallel lines have the same slope.Parallel lines will NEVER have the same
y-intercept.The slope of all vertical lines is
undefined. (No Slope)The slope of all horizontal lines is zero.
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Perpendicular Lines Lines that form a 90° Angle.Perpendicular Lines CAN have the same
y-intercept IF that is where they cross.Perpendicular Lines have slopes that are
negative reciprocals.– This means to change the sign and flip the
slope.Ex. If line “m” has a slope of 5, then it’s
negative reciprocal is
15
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You try it!!IF line “p” has a
slope of -2, then a line to it has a slope of ……
For line “n” the slope is the slope is...
12
REMEMBERChange the sign
AndFlip it over.
13
31
3
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Let’s compare Vertical and Horizontal Lines.Vertical lines are ┴ to horizontal
lines. AND
Horizontal lines are ┴ to vertical lines.
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0m
m undefined
Examples
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Name the slope of each line, thenGive the PARALLEL slope and thePERPENDICULAR slope.
Equation m // m m y = 3x + 5
7x + y = 4
y = 2
x = -4
3 3 13
7 4y x 7 7 17
0 0 .Undef
.Undef .Undef 0
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Why do we need to be able to identify the Parallel & Perpendicular Slopes?
So that we can write equations for new lines.– Either lines that are Parallel– OR lines that are Perpendicular
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HOW?– 1. Name the slope of the line you are given.– 2. List the new slope.– 3. Use the new slope and the point you are
given in the slope-intercept formula to write a new equation.
Example 5
3 4y x 5. 3m
Write an equation that is PARALLEL to the given line passing through the given point.
// 3m; (1,5)
y mx b ( , )x y5 ( 3) (1) b
3 b533b8
y mx b y
New //Equation 3x 8
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Write an equation that is PARALLEL to the given line passing through the given point.
6. 6 4x y ; ( 2,3)To get the
Slope, solveFor “y”
6x 6x6 4y x
6m // 6m•Find the PRGM key on your calculator.•Select program ASLOPE
•Which option? •#2 because you have a point and a slope.•Enter NEW (parallel) slope•Enter X and Y from your ordered pair
6 9y x
Parallel LinesHave SAME
Slope (m)
But…
DIFFERENTY-int.(b)
Example 6
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7. x = 5; (3, 4)Choose program ASLOPEOption #2– Name the slope
• Undefined – No number value – so…..– Name the “x” coordinate in the ordered
pair.
Parallel LinesHave SAME
Slope (m)
Both are Undefined
But…
DIFFERENTY-int.(b)
No y-int, but different “x”
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8. y = 3x – 2; (6, -1)Choose program ASLOPEOption #2
– Name the slope of this line but do not type it in.• m = 3• What is perpendicular to 3?• - 1/3
– type this one in because you are looking for a perpendicular equation.
– Enter the X and Y from the ordered pair.
Write an equation that is PERPENDICULAR to the given line passing through the given point.
1 13
y x
Perpendicular LinesHave
OPPOSITESlope (m)
AND….
DIFFERENTY-int.(b)
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Write an equation that is PERPENDICULAR to the given line passing through the given point.
9. 5 2 6x y ; (4, 2)To get the
Slope, solveFor “y”
5x 5x
5 32
y x 52
m 25
m
•Find the PRGM key on your calculator.•Select program ASLOPE
•Which option? •#2 because you have a point and a slope.•Enter NEW (perpendicular) slope•Enter X and Y from your ordered pair2 2
5 5y x
Perpendicular LinesHave
OPPOSITESlopes (m)
AND….
DIFFERENTY-int.(b)
2 2 22 5 6y x
Example 9
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10. y = 8; (-2, 8)Choose program ASLOPEOption #2– Name the slope
• ZERO – but don’t enter it yet.– What is perpendicular to ZERO?
• Undefined – has no number value so…
– Name the “x” coordinate in the ordered pair.
PerpendicularLinesHave
OPPOSITESlopes (m)
AND…
DIFFERENTY-int.(b)
No y-int, but “x”-int.
Example 10