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Parallel Lines - Printable Mathematics Worksheets kindergarten - Wayground

Parallel Lines

15 questions

9th - 9th Grade

Mathematics

This Grade 9 mathematics worksheet develops students’ ability to identify and write equations of lines parallel to a given line. Students work with lines in slope-intercept form and standard form, determine that parallel lines have equal slopes, and use a given coordinate point to calculate the correct y-intercept. The worksheet includes 15 questions: 13 multiple-choice items and 2 multiple-select items. The questions require students to recognize parallel slopes, rewrite equations when needed, test whether line pairs are parallel, and construct equations that pass through specified points. This makes the worksheet useful for guided practice, independent work, or a focused check of understanding after instruction on slope and linear equations. It is a free printable worksheet with a complete answer key, and it is also available as a digital quiz on Wayground.

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Worksheets

Parallel Lines

Total questions: 15

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 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

4.

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

a)

y=−52x−2y=-\frac{5}{2}x-2

b)

y=−52x−8y=-\frac{5}{2}x-8

c)

y=−52x+8y=-\frac{5}{2}x+8

d)

y=25x+195y=\frac{2}{5}x+\frac{19}{5}

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.

Two lines that are parallel will have ...

a)

Slope that is opposite reciprocals

b)

No slope

c)

Slope that is the same

d)

none of the above

8.
What slope is parallel to:  
m = 3/4
a)
4/3
b)
3/4
c)
-3/4
d)
-4/3
9.

Write an equation for the line parallel to y = 2x - 4 that passes through (1, 2).

a)

y = 2x - 3

b)

y = 2x - 4

c)

y = 2x + 4

d)

y = 2x

10.

Write an equation for the line parallel to y = 4x that passes through (1, 0).

a)

y = 4x + 4

b)

y = 4x - 4

c)

y = 4x + 1

d)

y = 4x - 1

11.

Write an equation for the line parallel to y = -2x + 2 that passes through (-1, -1).

a)

y = -2x - 1

b)

y = -2x + 1

c)

y = -2x - 3

d)

y = -2x + 3

12.

Write an equation for the line parallel to y = -x + 1 that passes through (-5, 2).

a)

y = -x - 7

b)

y = -x + 3

c)

y = -x + 7

d)

y = -x - 3

13.

Write an equation for the line parallel to y = -3x + 4 that passes through (1, 5).

a)

y = -3x - 2

b)

y = -3x + 8

c)

y = -3x + 2

d)

y = -3x - 8

14.

Write an equation for the line parallel to y = 3x + 5 that passes through (2, 4).

a)

y = 3x - 10

b)

y = 3x - 2

c)

y = 3x + 6

d)

y = 3x - 4

15.

Write an equation for the line parallel to y = 2x + 5 that passes through (3, 4).

a)

y = 2x - 2

b)

y = 2x + 10

c)

y = 2x + 2

d)

y = 2x - 5

Answer Key

Parallel Lines

Total questions: 15

1.
b)

y=2x−5y=2x-5

2.
b)

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

3.
b)

y = 3x + 2

4.
b)

y=−52x−8y=-\frac{5}{2}x-8

5.
d)

None are parallel.

6.
c)

−10y−2x=0-10y-2x=0

, b)

x + 5y=2x\ +\ 5y=2

7.
c)

Slope that is the same

8.
b) 3/4
9.
d)

y = 2x

10.
b)

y = 4x - 4

11.
c)

y = -2x - 3

12.
d)

y = -x - 3

13.
b)

y = -3x + 8

14.
b)

y = 3x - 2

15.
a)

y = 2x - 2

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FAQs

What does the Parallel Lines worksheet help Grade 9 students learn?

This worksheet helps students write equations of lines parallel to a given line while passing through a specified point. Its 13 multiple-choice and 2 multiple-select questions require students to preserve the original slope, convert some standard-form equations to identify that slope, calculate the new y-intercept, and recognize parallel line pairs.

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

Begin by reviewing that nonvertical parallel lines have the same slope, then model substituting a given point into y = mx + b to find the new intercept. Use the worksheet’s standard-form items to discuss how students can rewrite an equation before comparing slopes, and have students explain why the selected equation passes through the stated point. Finish with the multiple-select items as a check on whether students can compare slopes across several equations.

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

Students may choose an opposite reciprocal instead of the same slope, confusing parallel lines with perpendicular lines. They may also keep the original y-intercept rather than calculate a new one from the given point, or make sign and fraction errors when rewriting standard-form equations such as 5x + 2y = 1. In the multiple-select questions, check that students compare the slopes of both selected lines rather than relying on their visual appearance or selecting an unsupported pair.

How do I assign and grade this Parallel Lines worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for all 15 questions. For printable submissions, you can grade student work by scanning it with the Wayground for Teachers app.

How can I differentiate this parallel-lines worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing or choose a larger font size to make the slope-and-equation choices easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language while students work through the equation-writing and line-comparison items.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all 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.

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