Wayground
Writing equations of parallel and perpendicular lines - Printable Math Worksheets year 11 - Wayground

Writing equations of parallel and perpendicular lines

Wendi Miller

Created by Wendi Miller

24 questions

9th - 12th Grade

Math

Updated Sept 2026

This Grade 9–12 mathematics worksheet develops students’ ability to write equations of lines parallel or perpendicular to a given line through a specified point. Students analyze slopes, use equal slopes for parallel lines, find negative reciprocal slopes for perpendicular lines, and work with equations written in both slope-intercept and standard form. The 24-question set includes 18 multiple-choice questions, 4 multiple-select questions, and 2 matching questions. Items ask students to determine whether lines are parallel, perpendicular, or neither; identify appropriate slopes; and construct equations such as a line through a given coordinate. This free printable worksheet includes a complete answer key for instruction, independent practice, or assessment.

Worksheet settings

Font size

S
M
L
XL
WaygroundWorksheets

Writing equations of parallel and perpendicular lines

Total questions: 24

Name
Class
Date
1.

Write the equation of a line PARALLEL to y = 2x + 3 that passes through the point (3, 1).

a)

y=2x −3y=2x\ -3

b)

y=2x−5y=2x-5

c)

y=2x + 1y=2x\ +\ 1

d)

y=−12x+52y=-\frac{1}{2}x+\frac{5}{2}

2.

Write the equation of a line PARALLEL to that passes through the point (3, 1).  y=−52x+10y=-\frac{5}{2}x+10  

a)

y=−52x + 6y=-\frac{5}{2}x\ +\ 6  

b)

y =−52x+172y\ =-\frac{5}{2}x+\frac{17}{2}  

c)

y=25x+6y=\frac{2}{5}x+6  

d)

y=25x+ 8y=\frac{2}{5}x+\ 8  

3.

Write the equation of a line PERPENDICULAR to y = -2x + 1 that passes through the point (2, 3).

a)

y=−12x+12y=-\frac{1}{2}x+\frac{1}{2}

b)

y=12x+2y=\frac{1}{2}x+2

c)

y=−2x+7y=-2x+7

d)

y=−2x+8y=-2x+8

4.

Write the equation of a line PERPENDICULAR to y=13x−9y=\frac{1}{3}x-9  that passes through the point (-6, 10).

a)

y=13x−9y=\frac{1}{3}x-9

b)

y=13x+10y=\frac{1}{3}x+10

c)

y=−3x+6y=-3x+6

d)

y=−3x−8y=-3x-8

5.

Select the two lines that are parallel.

a)

y=4x−2y=4x-2

b)

y=−14xy=-\frac{1}{4}x

c)

y=−4x+1y=-4x+1

d)

None are parallel.

6.

Select the two lines that are parallel.

a)

y=5x−3y=5x-3

b)

x + 5y=2x\ +\ 5y=2

c)

−10y−2x=0-10y-2x=0

d)

None are parallel

7.

Select the two lines that are perpendicular.

a)

y=4x−2y=4x-2

b)

y=−14xy=-\frac{1}{4}x

c)

y=−4x+1y=-4x+1

d)

None are perpendicular.

8.

Select the two lines that are perpendicular.

a)

2x+6y=−32x+6y=-3

b)

−1.5y+4.5x=6-1.5y+4.5x=6

c)

y=−4x+1y=-4x+1

d)

None are perpendicular.

9.
Are these two lines parallel, perpendicular or neither?
y = -1/3x - 5
y = 1/3x + 2
a)
Parallel
b)
Perpendicular
c)
Neither
10.
A line is perpendicular to    y = 2x - 7.
What is the slope of this line? 
a)
-2
b)
1/2
c)
-1/2
d)
2
11.
What slope is parallel to:  
m = 4
a)
4
b)
-1/4
c)
-4
d)
1/4
12.
What slope is perpendicular to:  
m = 5/8
a)
-5/8
b)
5/8
c)
-8/5
d)
8/5
13.

Write the equation of a line PARALLEL to 3x - y = 2 that passes through the point (1, 5).

a)

y = 3x - 14

b)

y = 3x + 2

c)

y=13x+6y=\frac{1}{3}x+6

d)

y=13x−4y=\frac{1}{3}x-4

14.
What is the slope of a line parallel to the line whose equation is:  -2x + y = - 7?
a)
-2
b)
1/2
c)
-1/2
d)
2
15.
y = 5/7x +2
y = 5/7x - 30
These lines are...
a)
Parallel
b)
Perpendicular
c)
Neither
16.
y = -2/3x + 2
y = 3/2x + 9
These lines are...
a)
Parallel
b)
Perpendicular
c)
Neither
17.
Are the two linear equations parallel, perpendicular, or neither?

Are the two linear equations parallel, perpendicular, or neither?

a)

Parallel

b)

Perpendicular

c)

Neither

18.
Are the two linear equations parallel, perpendicular, or neither?

Are the two linear equations parallel, perpendicular, or neither?

a)

Parallel

b)

Perpendicular

c)

Neither

19.
Are the two linear equations parallel, perpendicular, or neither?

Are the two linear equations parallel, perpendicular, or neither?

a)

Parallel

b)

Perpendicular

c)

Neither

20.

Match the following

Match the following

Parallel lines

Match the following

Perpendicular lines

Match the following

Intersecting lines

21.

Match the following opposite reciprocal

-2/3

3/2

5/4

-4/5

15/4

-4/15

-7/5

5/7

22.
Write a linear equation in standard form.

Write a linear equation in standard form.

a)

2x-y = -3

b)

2x+y = 3

c)

2x-y = 3

d)

3x-y = 4

23.
Write a linear equation in standard form.

Write a linear equation in standard form.

a)

3x - y = - 5

b)

5x - y = 3

c)

2x - y = - 3

d)

5x - y = - 3

24.

Which equation in standard form has a graph that passes through the point (−4,2)\left(-4,2\right) and has a slope of 92\frac{9}{2} ?

a)

9x−2y=369x-2y=36

b)

9x−2y=269x-2y=26

c)

9x−2y=−409x-2y=-40

d)

9x−2y=−109x-2y=-10

WaygroundAnswer Key

Writing equations of parallel and perpendicular lines

Total questions: 24

1.
b)

y=2x−5y=2x-5

2.
b)

y =−52x+172y\ =-\frac{5}{2}x+\frac{17}{2}  

3.
b)

y=12x+2y=\frac{1}{2}x+2

4.
d)

y=−3x−8y=-3x-8

5.
d)

None are parallel.

6.
c)

−10y−2x=0-10y-2x=0

, b)

x + 5y=2x\ +\ 5y=2

7.
a)

y=4x−2y=4x-2

, b)

y=−14xy=-\frac{1}{4}x

8.
a)

2x+6y=−32x+6y=-3

, b)

−1.5y+4.5x=6-1.5y+4.5x=6

9.
c) Neither
10.
c) -1/2
11.
a) 4
12.
c) -8/5
13.
b)

y = 3x + 2

14.
d) 2
15.
a) Parallel
16.
b) Perpendicular
17.
b)

Perpendicular

18.
a)

Parallel

19.
b)

Perpendicular

20.
 - 

Parallel lines

,  - 

Perpendicular lines

,  - 

Intersecting lines

21.

-2/3

 - 

3/2

, 

5/4

 - 

-4/5

, 

15/4

 - 

-4/15

, 

-7/5

 - 

5/7

22.
b)

2x+y = 3

23.
a)

3x - y = - 5

24.
c)

9x−2y=−409x-2y=-40

Browse by subjects

Browse by grades

Browse by format

FAQs

What does this worksheet cover, and how does it help students learn to write equations of parallel and perpendicular lines?

This worksheet uses 24 multiple-choice, multiple-select, and matching items to practice identifying parallel, perpendicular, or neither relationships and writing a line equation through a given point. Students apply equal slopes for parallel lines, negative reciprocal slopes for perpendicular lines, and convert standard-form equations when determining the required slope.

How can I use this worksheet to teach writing equations of parallel and perpendicular lines?

Begin by reviewing how to identify slope from slope-intercept and standard-form equations, then model one item that asks for a parallel line through a point and one that asks for a perpendicular line. Have students explain why a slope stays the same for parallel lines or becomes its negative reciprocal for perpendicular lines before completing the classification and equation-writing items independently. Use the multiple-select and matching questions for partner discussion and justification.

What mistakes should I watch for when students complete this worksheet?

Students may use the negative reciprocal when a question asks for a parallel line, or keep the same slope when it asks for a perpendicular line. They may also misread the slope after rearranging a standard-form equation, make sign errors when substituting the given point, or choose only one option on the multiple-select items that ask students to identify line relationships. Check that students distinguish between finding a slope and using that slope to write the complete equation.

How do I assign and grade this parallel and perpendicular lines worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for the slope, classification, and equation-writing items. For printable submissions, you can scan student work with the Wayground for Teachers app to help grade responses.

How can I differentiate this worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing and font size to make the equations, coordinate points, multiple-select choices, and matching items easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language while keeping the same parallel and perpendicular line practice.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

© 2026 Wayground Inc.

Accessibility and Inclusion