Find the slope of a line Parallel to y=3x+5
Slopes of Parallel Lines
1. Solve the equation for y.(Already done in this case)
y=3x+5
This puts the equation in Slope intercept form soSlope is # in front of x.
Ans. Is 3
Find the slope of a line Parallel to y=2x+9
Slopes of Parallel Lines
1. Solve the equation for y.1. Solve the equation for y.(Already done in this case)
Ans. Is 2
y=2x+9
Find the slope of a line Parallel to 2y=8x+16
Slopes of Parallel Lines
1. Solve the equation for y.1. Solve the equation for y.
Find the slope of a line Parallel to 2y=8x+16
Slopes of Parallel Lines
1. Solve the equation for y.1. Solve the equation for y.
Ans. Is 4
2y=8x+16
2 22
y=4x+8
Find the slopes of a line Parallel to:
2.
€
y = 5x −1
3.
€
y = −3
7x − 3
4.
€
y =2
9x − 88
5.
€
4y = 5x −11
6.
€
3x = −y − 3
Find the slopes of a line Parallel to:
2.
€
y = 5x −1
3.
€
y = −3
7x − 3
4.
€
y =2
9x − 88
5.
€
4y = 5x −114 4 4
€
y =5
4x
−11
4
Find the eq. of a line Parallel to y=3x+5 andThrough Point (4,3) Equations of Parallel Lines
1. Solve the equation for y tofind slope.(Already done in this case)
y=3x+5
Slope Is 3
y=3x+5
Find the eq. of a line Parallel to y=3x+5 andThrough Point (4,3) Equations of Parallel Lines
1. Solve the equation for y tofind slope.
2. Put slope & (x,y) point into y=mx+b to find b.
y=3x+5
Slope Is 3
x y
y=3x+5
3=3(4)+b3=12+b
-9=b
-12 -12
Find the eq. of a line Parallel to y=3x+5 andThrough Point (4,3) Equations of Parallel Lines
1. Solve the equation for y tofind slope.
2. Put slope & (x,y) point into y=mx+b to find b.
3. Put m&b (from steps 1&2)into y=mx+b
To put equation into Standard Form, Bust Fractions & Move the x-term to the left. (Any Multiple of Eq is OK)
y=3x+5
3=3(4)+b3=12+b
-9=b
Slope Is 3
-12 -12
x y
y=3x-9
1.
2.
3.
Find the eq. of a line Parallel to y=-2x+6 andThrough Point (5,1) Equations of Parallel Lines
1. Solve the equation for y tofind slope.
2. Put slope & (x,y) point into y=mx+b to find b.
3. Put m&b (from steps 1&2)into y=mx+b
Find the equation of a line Parallel to given line and through Pt:
1. (4,-2)
€
y =9
5x − 3
2. (-3,-6)
€
4y = 5x −11
3. (5,8)
€
3x = −y − 3
•
•
(3,2)
(6,4)
(0,0) 1 2 3
1
2
4
3
5 6
4
€
slope =rise
run=
2
3
€
slope =rise
run=
−3
2
23
-3
2
PerpendicularLine
Solving for the equation of a line perpendicular to another line &
through the point (0,-3).
• (0,-3)
Given liney=x+3
Find the slope of a line Perpendicular to y=3x+5
Slopes of Perpendicular Lines
1. Solve the equation for y.
Find the slope of a line Perpendicular to y=3x+5 Slopes of Perpendicular Lines
1. Solve the equation for y.(Slope is Neg. Reciprocal)
y=3x+5
Perpendicular slope is -1/3
Find the slope of a line Perpendicular to y=2x+9
Slopes of Perpendicular Lines
1. Solve the equation for y.
Find the slopes of a line Perpendicular to:
1.
€
y =9
5x − 3
2.
€
y = 5x −1
3.
€
y = −3
7x − 3
4.
€
y =2
9x − 88
5.
€
4y = 5x −11
6.
€
3x = −y − 3
Find the eq. of a line Perpendicular to y=3x+5 andThrough Point (4,3) Equations of Perpendicular Lines
Find the eq. of a line Perpendicular to y=3x+5 andThrough Point (4,3) Equations of Perpendicular Lines
1. Solve the equation for y tofind slope. (Slope is Neg. Reciprocal)
y=3x+5
Slope Is 3Neg RecipIs -1/3
y=3x+5
Find the eq. of a line Perpendicular to y=3x+5 andThrough Point (4,3) Equations of Perpendicular Lines
1. Solve the equation for y tofind slope. (Use Neg Recip)
2. Put slope & (x,y) point into y=mx+b to find b.
y=3x+5
x y
y=3x+5
+4/3
€
3 = −1
34( ) + b
3 = −4
3+ b
41
3= b
+4/3
Slope Is 3Neg RecipIs -1/3
Find the eq. of a line Perpendicular to y=3x+5 andThrough Point (4,3) Equations of Perpendicular Lines
1. Solve the equation for y tofind slope. (Use Neg Recip)
2. Put slope & (x,y) point into y=mx+b to find b.
3. Put m&b (from steps 1&2)into y=mx+b
To put equation into Standard Form, Bust Fractions & Move the x-term to the left. (Any Multiple of Eq is OK)
y=3x+5
x y
+4/3
€
3 = −1
34( ) + b
3 = −4
3+ b
41
3= b
+4/3
€
y = −1
3x + 4
1
3
Slope Is 3Neg RecipIs -1/3
Find the eq. of a line Perpendicular to y=-2x+6 andThrough Point (5,1) Equations of Perpendicular Lines
1. Solve the equation for y tofind slope. (Use Neg Recip)
2. Put slope & (x,y) point into y=mx+b to find b.
y=-2x+6
x y
-5/2
€
1 =1
25( ) + b
1 =5
2+ b
−3
2= b
-5/2
Slope Is -2Neg Recip
Is 1/2
Find the eq. of a line Perpendicular to y=-2x+6 andThrough Point (5,1) Equations of Perpendicular Lines
Find the eq. of a line Perpendicular to y=-2x+6 andThrough Point (5,1) Equations of Perpendicular Lines
1. Solve the equation for y tofind slope. (Use Neg Recip)y=-2x+6
Slope Is -2Neg Recip
Is 1/2
Find the eq. of a line Perpendicular to y=-2x+6 andThrough Point (5,1) Equations of Perpendicular Lines
1. Solve the equation for y tofind slope. (Use Neg Recip)
2. Put slope & (x,y) point into y=mx+b to find b.
y=-2x+6
x y
-5/2
€
1 =1
25( ) + b
1 =5
2+ b
−3
2= b
-5/2
Slope Is -2Neg Recip
Is 1/2
Find the eq. of a line Perpendicular to y=-2x+6 andThrough Point (5,1) Equations of Perpendicular Lines
1. Solve the equation for y tofind slope. (Use Neg Recip)
2. Put slope & (x,y) point into y=mx+b to find b.
3. Put m&b (from steps 1&2)into y=mx+b
To put equation into Standard Form, Bust Fractions & Move the x-term to the left. (Any Multiple of Eq is OK)
y=-2x+6
x y
-5/2
€
1 =1
25( ) + b
1 =5
2+ b
−3
2= b
-5/2
€
y =1
2x +
−3
2
Slope Is -2Neg Recip
Is 1/2
Find the equation of a line Perpendicular to given line and
through Pt:
1. (4,-2)
€
y =9
5x − 3
2. (-3,-6)
€
4y = 5x −11
3. (5,8)
€
3x = −y − 3
Find the equation of a line Perpendicular to given line and
through Pt:
1. (4,-2)
€
y =9
5x − 3
2. (-3,-6)
€
4y = 5x −11
3. (5,8)
€
3x = −y − 3
Review Parallel Lines
•Parallel lines have the same slope•To find the slope of a parallel line solve equation for y•To find the equation of a parallel line
•Solve for y to get slope (m)•Put m and (x,y) point into y=mx+b to get b.•Put m & b back into y=mx+b (leave x&y)
Review Perpendicular Lines
•Perpendicular lines have the negative reciprocal slope•To find the slope of a perpendicular line solve equation for y•To find the equation of a perpendicular line
•Solve for y to get slope (negative reciprocal)•Put m and (x,y) point into y=mx+b to get b.•Put m & b back into y=mx+b (leave x&y)
Parallel Lines
•Parallel lines have the same slope•To find the slope of a parallel line solve equation for y•To find the equation of a parallel line
•Solve for y to get slope (m)•Put m and (x,y) point into y=mx+b to get b.•Put m & b back into y=mx+b (leave x&y)
Perpendicular Lines
•Perpendicular lines have the negative reciprocal slope•To find the slope of a perpendicular line solve equation for y•To find the equation of a perpendicular line
•Solve for y to get slope (negative reciprocal)•Put m and (x,y) point into y=mx+b to get b.•Put m & b back into y=mx+b (leave x&y)
Parallel Lines
Perpendicular
LinesFind the eq. of a line Perpendicular to y=-2x+6 andThrough Point (5,1) Equations of Perpendicular Lines
1. Solve the equation for y tofind slope. (Use Neg Recip)
2. Put slope & (x,y) point into y=mx+b to find b.
3. Put m&b (from steps 1&2)into y=mx+b
y=-2x+6
x y
-5/2
€
1 =1
2
5( ) + b
1 =5
2
+ b
− 3
2
= b
-5/2
€
y =1
2x +
− 3
2
-2Slope Is Neg Recip
Is 1/2
Find the eq. of a line Parallel to y=3x+5 andThrough Point (4,3) Equations of Parallel Lines
1. Solve the equation for y tofind slope.
2. Put slope & (x,y) point into y=mx+b to find b.
3. Put m&b (from steps 1&2)into y=mx+b
y=3x+5
3=3(4)+b3=12+b
-9=b
Slope Is 3
-12 -12
x y
y=3x-9
1.
2.
3.
Find the slope of a line Parallel to 2y=8x+16
Slopes of Parallel Lines
1. Solve the equation for y.1. Solve the equation for y.
Ans. Is 4
2y=8x+16
2 22
y=4x+8
How to remember Perpendicular Lineshave NEG-RECIPROCAL Slopes
Find the slope of a line Perpendicular to y=3x+5 Slopes of Perpendicular Lines
1. Solve the equation for y.(Slope is Neg. Reciprocal)
y=3x+5
Perpendicular slope is -1/3
•
•
(3,2)
(6,4)
(0,0) 1 2 3
1
2
4
3
5 6
4
€
slope =
rise
run
=
2
3
€
slope =
rise
run
=
− 3
2
23
-32
PerpendicularLine