Parallel & Perpendicular Lines

Parallel Lines have the same Slope

(or same Rise/Run)

Finding the Slope of a Line Parallel to another Line is a

No Brainer

Find the slope of a line Parallel to y=3x+5

Slopes of Parallel Lines

Find the slope of a line Parallel to y=3x+5

Slopes of Parallel Lines

1. Solve the equation for y.

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.

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 slope of a line Parallel to:

1.

€

y =9

5x − 3

Find the slopes of a line Parallel to:

1.

€

y =9

5x − 3

ANSWER IS 9/5

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

6.

€

3x = −y − 3+3+3

€

3x + 3 = −y-1-1 -1

€

−3x − 3 = y

1. Solve the equation for y.

Given the equation of one line

y=1/2x+1 •(0,1)

Find the equation of a parallel line through a point

y=1/2x+1

•(2,-1)

Find the eq. of a line Parallel to y=3x+5 andThrough Point (4,3) Equations of Parallel Lines

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

Slopes of Perpendicular Lines

NEG RECIPROCAL(Double Switch)

•

•

(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

How to remember Perpendicular Lines have NEG-RECIPROCAL Slopes

How to remember Perpendicular Lines have NEG-RECIPROCAL Slopes

Perpendicular Lines have NEG-RECIPROCAL Slopes

What is the NEG-RECIPROCAL

€

m =2

31.

What is the NEG-RECIPROCAL

€

m =2

31.

-32

What is the NEG-RECIPROCAL

2.

€

m = −5

3

What is the NEG-RECIPROCAL

2.

€

m = −5

3 35

What is the NEG-RECIPROCAL

3.

€

m =7

−8

What is the NEG-RECIPROCAL

3.

€

m =7

−8 87

What is the NEG-RECIPROCAL

4.

€

m = 7

What is the NEG-RECIPROCAL

4.

€

m = 7

-17

What is the NEG-RECIPROCAL

5.

6.€

m = −10

€

m =−9

5

What is the NEG-RECIPROCAL

5.

6.€

m = −10

€

m =−9

5

11059

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

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