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Writing an Equation from Two Points - Printable Mathematics Worksheets - Wayground

Writing an Equation from Two Points

15 questions

7th - 9th Grade

Mathematics

This free printable mathematics worksheet helps students in Grades 7–9 write linear equations from two points. Across 15 multiple-choice questions, students calculate slope, determine the y-intercept, and select the matching equation in slope-intercept form. The set includes positive, negative, fractional, and undefined slopes, along with items that ask students to identify slope and y-intercept or use a given slope and point. Students strengthen their ability to connect coordinate pairs to the equation y = mx + b, substitute values accurately, and check whether an equation fits both given points. The multiple-choice format makes the worksheet useful for guided practice, independent review, or a quick assessment of line-equation skills. It includes a complete answer key so teachers can review errors efficiently and help students distinguish mistakes in slope, intercept, and sign. The worksheet is available as a free printable resource for classroom or homework use.

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Worksheets

Writing an Equation from Two Points

Total questions: 15

Name
Class
Date
1.
Find the equation of the line that passes through the points:

(-2, 4) and (1, 10)
a)
y = 2x - 1
b)
y = -2x + 1
c)
y = 2x
d)
y = -2x
2.
Find the equation of the line that passes through the points:

(2, 2) and (3, 4)
a)
y = 2x + 2
b)
y = -2x - 2
c)
y = -2x + 2
d)
y = 2x - 2
3.
Find the equation of the line that passes through the points:

(-3, 3) and (3, -1)
a)
y = -⅔ x + 1 
b)
y = -⅔ x  
c)
y = ⅔ x + 1 
d)
y = -⅔ x +3 
4.
Find the equation of the line that passes through the points:

(3, 4) and (0, -5)
a)
y = 3x + 5
b)
y = -3x + 4
c)
y = -3x + 4
d)
y = 3x - 5
5.
Find the equation of the line that passes through the points:
(0, -2) and (-5, 3)
a)
y = -x - 2
b)
y = x - 2
c)
y = x + 3
d)
y = -x - 3
6.
Find the equation of the line that passes through the points:
(-4, -2) and (-3, 5)
a)
y = 1/7 x + 26
b)
y = 7x + 26
c)
y = -7x + 26
d)
y = -7x - 26
7.
Find the equation of the line that passes through the points:
(4, -1) and (0, -3)
a)
y = 2x - 3
b)
y = -2x + 3
c)
y = ½ x - 3
d)
y = -½ x + 3
8.
Find the equation of the line that passes through the points:
(3, 3) and (1, -5)
a)
y = -9x + 4
b)
y = 4x - 9
c)
y = ¼ x + 9
d)
y = -9x - 4
9.
Find the equation of the line that passes through the points:
(5, 3) and (4, -3)
a)
y = 27x + 6
b)
y = -6x
c)
y = 6x - 27
d)
y = 6x + 27
10.
Find the equation of the line that passes through the points:
(0, -5) and (4, 3)
a)
y = 2x - 5
b)
y = 2x + 5
c)
y = 5x - 2
d)
y = 5x + 2
11.
Identify the slope and y-intercept of the equation below:
y = -3x + 5
a)
slope: -3
y-intercept: (0, -5) 
b)
slope: -3
y-intercept: (5, 0) 
c)
slope: -3
y-intercept: (0, 5) 
d)
slope: -3
y-intercept: (-5, 0) 
12.

Which of the following is the equation of the line that has a slope of 3 and passes through the point (-1, 9)?

a)

y = -3x + 12

b)

y = 3x + 3

c)

y = 3x + 12

d)

y = 3x - 3

13.

Write the linear equation that is solved by both (−6, 2) and (0, 4):

a)

y = (1/3)x + 4

b)

y = (-1/3)x + 4

c)

y = -3x + 4

d)

y = 3x + 4

14.

What is the equation of the line that goes through the points (2, 9) and (3, 1) ?

a)

y= 8x - 5

b)

y= -8x + 25

c)

y= (1/8)x - 2

d)

y= (-1/8)x + 1

15.
Find the slope of the line that passes through:
(5, -10) and (5, -4)
a)
undefined
b)
0
c)
- 14/10
d)
10/14
Answer Key

Writing an Equation from Two Points

Total questions: 15

1.
c) y = 2x
2.
d) y = 2x - 2
3.
a) y = -⅔ x + 1 
4.
d) y = 3x - 5
5.
a) y = -x - 2
6.
b) y = 7x + 26
7.
c) y = ½ x - 3
8.
b) y = 4x - 9
9.
c) y = 6x - 27
10.
a) y = 2x - 5
11.
c) slope: -3
y-intercept: (0, 5) 
12.
c)

y = 3x + 12

13.
a)

y = (1/3)x + 4

14.
b)

y= -8x + 25

15.
a) undefined

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FAQs

What does the “Writing an Equation from Two Points” worksheet cover?

This Grade 7–9 worksheet contains 15 multiple-choice questions on writing linear equations from two coordinate points. Students calculate the slope, find the y-intercept, and choose the matching equation in slope-intercept form, with additional items on identifying slope and intercept and recognizing an undefined slope.

How can I use this worksheet to teach writing an equation from two points?

Model one item by finding the slope from the two coordinate pairs, substituting a point into y = mx + b, and checking the resulting equation with the second point. Then have students explain why selected equations fit both points, using the later slope-and-intercept and given-slope items to connect the procedure to the structure of a linear equation.

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

Watch for students reversing the coordinate differences when calculating slope, losing the negative sign, or using the x-intercept instead of the y-intercept. Students may also choose an equation with the correct slope but incorrect constant term, or report a numerical slope for the final pair of points even though both x-coordinates are equal and the slope is undefined.

How do I assign and grade this worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, and it includes 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, while the digital quiz can be completed and graded online.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or choose a larger font so the coordinate pairs and multiple-choice answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language while keeping the line-equation practice intact.

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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