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Writing Equations of Lines - Printable Mathematics Worksheets - Wayground

Writing Equations of Lines

15 questions

9th - 12th Grade

Mathematics

This Grade 9–12 mathematics worksheet gives students 15 multiple-choice questions on writing equations of lines. It focuses on identifying slope and y-intercept from slope-intercept form, finding slope from two points, writing equations from a slope and a point, determining equations from two points, and recognizing vertical lines in the form x = a. Students also select equations when the slope or y-intercept is provided directly. The worksheet builds fluency with substituting coordinates, calculating slope accurately, determining the constant term, and checking whether an equation matches the stated conditions. Its varied question set helps teachers assess whether students can move between given information and the correct linear equation, including cases with negative or fractional slopes and vertical lines. It is suitable for guided practice, independent review, or a formative check in secondary mathematics. This free printable worksheet includes a complete answer key for efficient review and grading.

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Worksheets

Writing Equations of Lines

Total questions: 15

Name
Class
Date
1.
Given that the slope is  -4 and the y intercept is -4 what is the equation of the line?
a)
y = 4x - 4
b)
y = -4x - 4
c)
y = -4
d)
y = -4x + 4
2.
Identify the slope and y intercept in the equation of the line: y = -1/3x + 1
a)
Slope: 1/3
y-intercept: 1
b)
Slope: 1/3
y-intercept: -1
c)
Slope: -1/3
y-intercept: 1
d)
Slope: -1/3
y-intercept: 0
3.
Find the slope of the line that passes through
(10, 1) and (5, 2)
a)
1/5
b)
-1/5
c)
5
d)
-5
4.
Write the equation of the line with slope 4 through the point (-2, 5).
a)
y = 4x - 13
b)
y = 4x + 13
c)
y = 4x - 3
d)
y = 4x + 3
5.
Write the equation of the line with slope 3/5 through the point (20, 6).
a)
y = 3/5x - 6
b)
y = 3/5x +18
c)
y = 3/5x - 18
d)
y = 3/5x +6
6.
Write the equation of the line through the points (7, 8) and (-12, -11).
a)
y = x + 1
b)
y = x + 15
c)
y = -x - 1
d)
y = -x - 23
7.

Which of the following is the equation of the line that has a slope of 3 and passes through the point (0, 9)?

a)

y = -3x + 12

b)

y = 3(x + 9)

c)

y = 3x + 9

d)

y = 3x - 3

8.
Write equation of the line containing (-3,4) and (-1,-2)
a)
y = -3x - 5
b)
y = -3x + 1
c)
y = -3x + 13
d)
y = 3x + 1
9.

Write equation of a vertical line containing (2,6)

a)

y = 5x - 14

b)

y = 2

c)

x = 2

d)

y = -5x + 6

10.
Write equation of the line containing (-1,-3) and (1,1)
a)
y = -2x + 1
b)
y = 2x -1
c)
y = 2x + 7
d)
y = -2x - 1
11.
Write the slope-intercept form of the equation with the given point and slope.
Through (2,5)  and m= 1/2
a)
y=1/2x+4
b)
y=-1/2x-4
c)
y=4x-1/2
12.
Write the slope-intercept form of the equation with the given point and slope.
Through (-1,4)  and m= -3
a)
y=x-3
b)
y=-3x+1
c)
y=x+2
13.
Write the slope-intercept form of the equation with the given point and slope.
Through (1,5)  and m= 3
a)
y=3x+2
b)
y=3x-2
c)
y=2x+3
14.
Which is the equation of the line with y-intercept -2 and slope 6.
a)
y = -2x + 6
b)
y = 3x
c)
y = -2x - 6
d)
y = 6x - 2
15.

What is the equation of a vertical line through the point (3, 2)?

a)

y = x + 6

b)

y = 3

c)

x = 3

d)

y = -x + 1

Answer Key

Writing Equations of Lines

Total questions: 15

1.
b) y = -4x - 4
2.
c) Slope: -1/3
y-intercept: 1
3.
b) -1/5
4.
b) y = 4x + 13
5.
a) y = 3/5x - 6
6.
a) y = x + 1
7.
c)

y = 3x + 9

8.
a) y = -3x - 5
9.
c)

x = 2

10.
b) y = 2x -1
11.
a) y=1/2x+4
12.
b) y=-3x+1
13.
a) y=3x+2
14.
d) y = 6x - 2
15.
c)

x = 3

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FAQs

What does the Writing Equations of Lines worksheet cover?

This worksheet uses 15 multiple-choice questions to assess writing and interpreting linear equations in slope-intercept form. Students identify slope and y-intercept, calculate slope from two points, write an equation from a slope and one point or from two points, and recognize vertical-line equations such as x = 2 or x = 3.

How can I use this worksheet to teach students to write equations of lines?

Model the progression used in the worksheet: identify m and b when they are given, calculate slope from coordinate pairs, and then substitute a known point to determine the y-intercept. Before students complete the multiple-choice items, have them explain why a candidate equation satisfies both the stated slope and point, and separately emphasize that a vertical line is written as x = a rather than in slope-intercept form.

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

Students may reverse the coordinate differences when calculating slope, lose the negative sign, or confuse the y-intercept with the slope in an equation such as y = -1/3x + 1. When using a point and slope, they may choose the wrong constant term, and when identifying vertical lines through (2, 6) or (3, 2), they may incorrectly select a y-value or try to assign a finite slope.

How do I assign and grade this Writing Equations of Lines worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, with a complete answer key for all 15 multiple-choice questions. You can grade printable submissions by scanning student work with the Wayground for Teachers app, or review responses through the digital quiz.

How can I differentiate this worksheet for my students?

For the multiple-choice equation items, use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font size so expressions, fractions, and answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those options support access to the linear-equation practice.

Where can I find more worksheets like this on Wayground?

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

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