Writing Parallel and

Perpendicular Lines

Part 1

Parallel Lines // (symbol)

All parallel lines have the same slope. Parallel lines will NEVER CROSS. Since Parallel lines don’t cross, we say they have

NO solution. The slope of all vertical lines is undefined. (No

Slope) The slope of all horizontal lines is zero.

Given slope: Parallel slope:

2) y = 7

3A x

2

3m

) y = 4x 8B 4m

) y = 5 3C x 5m

7) y = 4

15D x

7

15m

now go to next column

1) Find line parallel to and goes through (-6, 4)

1 1( , )x y

y bmx

6( 6)4 b4 36 b

3636

b40

y bmx

__ __y x

6 40y x

6 40

6m

Step 1

Find m

From given eq.

Step 2

Find b

Plug in x,y, & m

Step 3

Find equation

Plug in m & b

6 4y x

y = 6x 4

now go to next column

2) Find line parallel to and goes

through (6, -2)

1 1( , )x y

y bmx 3

8

(6)2 b2 18

8

b

1818

b1

4

y bmx

__ __y x

3 1

8 4y x

3

8

1

4

3

8m

Step 1Find m—solve for y From given eq.

Step 2Find b

Plug in x,y, & m

Step 3Find equationPlug in m & b

3 8 8x y

3 8 8x y

3x 3x8 3 8y x

31

8y x

8 8 8

(8) (8) (8)

16 18 8b

8b28 8

Perpendicular Lines (symbol) Lines that form a 90° Angle. Perpendicular Lines have one solution written as an

ordered pair. Perpendicular Lines’ slopes are NOT the same

(negative reciprocals). Do 2 things…

FLIP the slope

& CHANGE the SIGN

m

3

2m

23

Given slope: Perpendicular slope:

5)

6mA

6

5m

1)

3B m

3

1m

3

4)

7C m 7

4

m

) 9D m 1

9m

now go to next column

3) Find line perpendicular to and goes through (-6, 4)

1 1( , )x y

3 ( 6)4 b4 18 b

1818b14

__ __y x

3 14y x

3 14

33

1m

Step 1 Step 2 Step 3

14

3y x

1

3y = x+4

FLIP the slope &

CHANGE the SIGN

now go to next column

4) Find line perpendicular to and goes through (4, 7)

1 1( , )x y

y bmx 2

5

(4)7 b

7 8

5 b

88

b27

5

y bmx

__ __y x

2 27

5 5y x

2

5

27

5

2

5m

Step 1 Step 2 Step 3

5 2 10x y

2 5 10x y

5x 5x2 5 10y x

55

2y x

2 2 2(5) (5) (5)

35 8 5b

5b275 5

FLIP the slope &

CHANGE the SIGN