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Write the Equation of a Line Using Two Given Points - Printable Mathematics Worksheets - Wayground

Write the Equation of a Line Using Two Given Points

8 questions

9th - 11th Grade

Mathematics

This free printable mathematics worksheet helps students in Grades 9–11 write the equation of a line from two given points. Across 8 multiple-choice questions, students determine the slope, calculate the y-intercept, and select the matching equation in slope-intercept form, including examples with positive and negative slopes and fractional values. Use it for guided practice, independent work, review, or a quick check of students’ ability to connect coordinate pairs with linear equations. The varied point pairs require students to attend to subtraction signs, simplify slopes accurately, and verify that a proposed equation fits both points rather than relying on a single calculation. A complete answer key is included with this free printable worksheet.

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Worksheets

Write the Equation of a Line Using Two Given Points

Total questions: 8

Name
Class
Date
1.

Find the equation of a line that passes through (-5, -1) and (1, -4).

a)

y = −12x − 72y\ =\ -\frac{\text{1}}{\text{2}}x\ -\ \frac{\text{7}}{\text{2}}

b)

y = 12x − 72y\ =\ \frac{1}{2}x\ -\ \frac{7}{2}

c)

y = 23x +14y\ =\ \frac{2}{3}x\ +\frac{1}{4}

d)

y = −23x +14y\ =\ -\frac{2}{3}x\ +\frac{1}{4}

2.

Find the equation of a line that passes through (5,1) and (-5,3).

a)

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

b)

y = −15x +2y\ =\ -\frac{1}{5}x\ +2

c)

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

d)

y = 15x + 2y\ =\ \frac{1}{5}x\ +\ 2

3.

Find the equation of a line that passes through (-1,0) and (5,5).

a)

y = -5x + 6

b)

y =56x − 56y\ =\frac{5}{6}x\ -\ \frac{5}{6}

c)

y = 56x + 56y\ =\ \frac{5}{6}x\ +\ \frac{5}{6}

d)

y = -6x + 5

4.

Find the equation of a line that passes through (-2,2) and (-5, -4).

a)

y = 3x + 6

b)

y = 2x + 6

c)

y = -2x + 6

d)

y = -3x + 6

5.

Find the equation of a line that passes through (5,3) and (4,5).

a)

y = -2 + 13

b)

y = 2x + 13

c)

y = 13

d)

y = -2x + 13

6.

Find the equation of a line that passes through (5,5) and (4,-5).

a)

y = 10x - 45

b)

y = 10x

c)

y = -10X - 45

d)

y = 10x + 45

7.

Find the equation of a line that passes through (5,1) and (1,3).

a)

y = 12+72y\ =\ \frac{1}{2}+\frac{7}{2}

b)

y = −12x + 72y\ =\ -\frac{1}{2}x\ +\ \frac{7}{2}

c)

y = −12+ 72y\ =\ -\frac{1}{2}+\ \frac{7}{2}

d)

y = 1x + 72y\ =\ 1x\ +\ \frac{7}{2}

8.

Find the equation of a line that passes through (4,-2) and (-4,-4).

a)

y = 14 − 3y\ =\ \frac{1}{4}\ -\ 3

b)

y = 14x +3y\ =\ \frac{1}{4}x\ +3

c)

y = 14x − 3y\ =\ \frac{1}{4}x\ -\ 3

d)

y = −14x − 3y\ =\ -\frac{1}{4}x\ -\ 3

Answer Key

Write the Equation of a Line Using Two Given Points

Total questions: 8

1.
a)

y = −12x − 72y\ =\ -\frac{\text{1}}{\text{2}}x\ -\ \frac{\text{7}}{\text{2}}

2.
b)

y = −15x +2y\ =\ -\frac{1}{5}x\ +2

3.
c)

y = 56x + 56y\ =\ \frac{5}{6}x\ +\ \frac{5}{6}

4.
b)

y = 2x + 6

5.
d)

y = -2x + 13

6.
a)

y = 10x - 45

7.
b)

y = −12x + 72y\ =\ -\frac{1}{2}x\ +\ \frac{7}{2}

8.
c)

y = 14x − 3y\ =\ \frac{1}{4}x\ -\ 3

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FAQs

What does this worksheet cover?

This worksheet covers writing a linear equation in slope-intercept form from two given coordinate points. Its 8 multiple-choice items require students to calculate the slope, find the y-intercept, and choose the equation that passes through both points, including equations with negative and fractional slopes.

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

Model one item by finding the change in y over the change in x, substituting a point to determine the y-intercept, and writing the result as y = mx + b. Then have students solve the remaining multiple-choice items while explaining why the selected equation fits both coordinates. Ask students to substitute both given points into a proposed equation to connect the algebraic result to the original line.

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

Watch for students reversing or mishandling the signs in the slope calculation, especially when both coordinates are negative or the slope is negative. Students may also use the slope as the y-intercept, omit the x in a slope-intercept equation, or stop after finding the slope without determining b. Encourage them to check the final equation with both given points before selecting an option.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground. It includes a complete answer key, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format also gives schools an option for reducing screen time while students practice calculating slopes and intercepts.

How can I differentiate this worksheet for my students?

For the multiple-choice line-equation items, use Advanced Settings to increase font size or spacing so coordinate pairs, fractions, and answer choices are easier to read. You can also select a dyslexia-friendly font or translate the worksheet into another language when that supports access to the instructions and mathematical prompts.

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 help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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