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Finding Equation of a Line from a Graph - Printable Mathematics Worksheets grade 9 - Wayground

Finding Equation of a Line from a Graph

21 questions

9th - 9th Grade

Mathematics

Finding Equation of a Line from a Graph is a Grade 9 mathematics worksheet that helps students interpret graphs and express linear relationships as equations. Students identify slope and y-intercepts, calculate slope from a graph, select matching slope-intercept equations, and write equations in the form y = mx + b. The worksheet also includes items on recognizing vertical lines such as x = 3 and x = -2, horizontal lines such as y = 3 and y = -1, and matching graphs to equations. The worksheet contains 21 questions: 20 multiple-choice items and one fill-in-the-blank question. Students use visual evidence from each graph—including rise, run, intercepts, and line direction—to distinguish equations with positive or negative slopes and different intercepts. This free printable worksheet includes a complete answer key, making it useful for guided practice, independent work, homework, or a quick Grade 9 skills check.

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Worksheets

Finding Equation of a Line from a Graph

Total questions: 21

Name
Class
Date
1.
 Identify the slope-intercept equation:
a)
y = 2x - 2
b)
y = -2x + 2
c)
y = -2x + 4
d)
y = 2x + 4
2.
Find the slope of the line.
a)
-5/4
b)
5/4
c)
-4/5
d)
4/5
3.
The equation of the following line is 
a)
x = 5
b)
x = 3
c)
x = 4
d)
x =7
4.

Which equation matches the graph? (Click me to see the image)

a)

y = -1/4x + 2

b)

y = 1/4x + 2

c)

y = 1x + 4

d)

y = 4x + 2

5.
Write the equation for the line in slope-intercept form.
a)
y=-1x+3
b)
y=4x+3
c)
y=¼x+3
d)
y=-4x+3
6.
Which equation is being represented by this line?
a)
y = -1x + 2
b)
y = 1/2x + 2
c)
y = 3x -4
d)
y = -3x +2
7.
What is the equation of this line?
a)
0
b)
undefined 
c)
y = -2
d)
x = -2
8.
What is the equation of the line graphed?
a)
x = -1
b)
y = -1
c)
y = -1x
d)
y = x - 1
9.

Which is the correct graph for x = -4?

a)

A

b)

B

c)

C

d)

D

10.

Which is the correct graph for y = 3?

a)

A

b)

B

c)

C

d)

D

11.
What is the slope of this line?
a)
2
b)
4
c)
1/2
d)
1/4
12.
 Identify the slope-intercept equation:
a)
y = 2x - 2
b)
y = -2x + 2
c)
y = -2x + 4
d)
y = 2x + 4
13.
 Identify the slope and y intercept to write an equation of the line.
a)
y = -1/4x + 2
b)
y = 1/4x + 2
c)
y = -4x + 2
d)
y = 4x - 2
14.

Which equation is best represented by this graph? Which\ equation\ is\ best\ represented\ by\ this\ graph?\

a)


y=−34x+3y=-\frac{3}{4}x+3

b)

y=34x+3y=\frac{3}{4}x+3

c)

y=4x+3y=4x+3

d)

y=−4x+3y=-4x+3

15.

Use the graph to write the equation of the line in slope intercept form?

(a)  

16.

Write an equation for the line shown by counting the slope and identifying the y-intercept.

a)

y = -2x + 2

b)

y = 2x + 2

c)

y = 1/2x- 2

d)

y = -1/2x + 2

17.

Identify the slope-intercept equation for the graph:

a)

y = 2x - 2

b)

y = -2x + 2

c)

y = -2x + 4

d)

y = 2x + 4

18.

Write the equation of the line.

a)

y=−x+3y=-x+3

b)

y=−3x+1y=-3x+1

c)

y=−13x−5y=-\frac{1}{3}x-5

d)

y=−3x−3y=-3x-3

19.

This graph has a positive gradient

a)

True

b)

False

20.

Work out the equation for this line

a)

y = 1/2 x + 4

b)

y = 2x + 4

c)

y = 4x - 2

d)

y = -2x + 4

21.

Work out the equation of this line

a)

y = 3/2x - 1

b)

y = 2/3x + 1.5

c)

y = -2/3x - 1

d)

y = 2/3x - 1

Answer Key

Finding Equation of a Line from a Graph

Total questions: 21

1.
d) y = 2x + 4
2.
a) -5/4
3.
b) x = 3
4.
b)

y = 1/4x + 2

5.
b) y=4x+3
6.
a) y = -1x + 2
7.
d) x = -2
8.
b) y = -1
9.
d)

D

10.
a)

A

11.
c) 1/2
12.
d) y = 2x + 4
13.
c) y = -4x + 2
14.
a)


y=−34x+3y=-\frac{3}{4}x+3

15.
y=2x-4
16.
d)

y = -1/2x + 2

17.
d)

y = 2x + 4

18.
d)

y=−3x−3y=-3x-3

19.
a)

True

20.
b)

y = 2x + 4

21.
d)

y = 2/3x - 1

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FAQs

What does this worksheet cover?

This Grade 9 worksheet focuses on writing and identifying linear equations from graphs in slope-intercept form, y = mx + b. Across 20 multiple-choice questions and one fill-in-the-blank item, students find slope and y-intercepts, match graphs to equations, and recognize vertical equations such as x = -2 and horizontal equations such as y = -1.

How can I use this worksheet to teach students to find an equation from a graph?

First model how to read the y-intercept and count rise over run from one of the worksheet’s graphs, then connect those values to y = mx + b. Have students explain why a line with a negative slope needs a negative m and why vertical and horizontal graphs are represented by x = a or y = b rather than slope-intercept equations. Students can then complete the matching and equation-writing items independently.

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

Watch for students reversing rise and run, choosing the wrong sign for the slope, or using the x-intercept when the question asks for the y-intercept. Students may also confuse vertical lines such as x = 3 with horizontal lines such as y = 3, or select a graph whose intercept is correct but whose slope is not. Ask them to verify both the slope and the intercept before choosing an equation.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key for all 21 questions. You can assign the digital version for online responses or print it for written graph analysis; printable submissions can be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this graph-to-equation worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the graph-based multiple-choice choices and equation-writing prompt are easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when appropriate for your learners.

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

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