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Writing Equations in 2 Variables - Printable Math Worksheets 6th - 8th Grade - Wayground

Writing Equations in 2 Variables

Kristen Barboza

Created by Kristen Barboza

14 questions

6th - 8th Grade

Math

Updated Oct 2026

Writing Equations in 2 Variables is a free printable mathematics worksheet for students in Grades 6–8. It contains 14 multiple-choice questions that ask students to translate real-world situations into equations with two variables, including starting values and rates, fixed fees and per-item costs, increases and decreases, and total or changing amounts. Contexts include savings, repairs, fundraising, printing, depreciation, food, memberships, shipping, and purchases. The worksheet also asks students to identify equations from tables and graphs, including relationships such as y = x + 4, y = 3x + 9, t = 10d, y = 2x, and y = 5x. Students must determine which number represents the starting value or multiplier and place each quantity correctly in the equation. The worksheet includes a complete answer key, making it useful for guided practice, independent review, or assessment of students’ ability to represent patterns and relationships algebraically.

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WaygroundWorksheets

Writing Equations in 2 Variables

Total questions: 14

Name
Class
Date
1.

Charlie is starting a savings account. He has saved $40 and he earns $7.50 per hour. Write an equation for the amount Charlie saves.

a)

40+7.50x=y40+7.50x=y

b)

40x+7.50=y40x+7.50=y

c)

40+7.50=y40+7.50=y

d)

40+17.50x=y40+17.50x=y

2.

Mr. Piper's plumbing needed repairs. The plumber charged $98 for parts plus $45 per hour for labor. Write an equation to find the total cost of repairs.

a)

98x+45=y98x+45=y

b)

98+45x=y98+45x=y

3.

The 30 members of a choir are trying to raise money to cover travel costs to a singing camp. They have already raised $600. Which equation would you solve to find the average amount each member can raise in order to meet the goal?

a)

30x+600=y30x+600=y

b)

30x−600=y30x-600=y

c)

x+600=30yx+600=30y

d)

30x=600y30x=600y

4.

The space club is having some posters printed. The printer charges $250 plus $2 per poster. Write an equation for the cost of the posters.

a)

250x+2=y250x+2=y

b)

y+2x=250y+2x=250

c)

250−2x=y250-2x=y

d)

2x+250=y2x+250=y

5.

Maggie buys a Chromebook for $200. It decreases in value each month by $20. Write an equation for the total value of the Chromebook.

a)


 20x+200=y20x+200=y  

b)

 20x−200=y20x-200=y  

c)

 200+20x=y200+20x=y  

d)

 200−20x=y200-20x=y  

6.

A cheese pizza costs $5. Additional toppings cost $1.50 each. Write an equation in two variables that represents the total cost of a pizza.

a)

y=5x+1.50y=5x+1.50

b)

y=5+1.50xy=5+1.50x

c)

1.5x+5y=81.5x+5y=8

d)

x+1.5y=5x+1.5y=5

7.

It costs $35 to join an art studio. The pottery class fee is $5. Write an equation in two variables that represents the total cost of the art studio.

a)


35x+5=y35x+5=y

b)

5x+35=y5x+35=y

8.

Picture frames from a frame website cost $50 each and $10 for shipping. Write an equation for the total cost of buying picture frames from this website.

a)

50x+10=y50x+10=y

b)

10x+50=y10x+50=y

9.
Which equation matches the table?
Which equation matches the table?
a)
y = x 
b)
y = 5x
c)
y = x - 4
d)
y = x + 4
10.
Which equation matches the table?
Which equation matches the table?
a)
y = 3x + 9
b)
y = x + 9 
c)
y = x + 3
d)
y = 12x - 3
11.
Write the equation of the line represented by this table.

Write the equation of the line represented by this table.

a)

y= 3x+5

b)

y = -3x + 5

c)

y= 8x - 1

d)

y = 3x + 14

12.
Write an equation that represents the relationship between the variables in the table.

Write an equation that represents the relationship between the variables in the table.

a)

t=10d

b)

t=d-9

c)

t=10-d

d)

d=t+10

13.
What equation is represented by the graph?

What equation is represented by the graph?

a)

y = x + 2

b)

y = 2x

c)

x = 2y

d)

y = x + (-2)

14.
What is the correct equation for the graph?

What is the correct equation for the graph?

a)

y = x + 5

b)

x = y

c)

y = 5x

d)

x = 5y

WaygroundAnswer Key

Writing Equations in 2 Variables

Total questions: 14

1.
a)

40+7.50x=y40+7.50x=y

2.
b)

98+45x=y98+45x=y

3.
a)

30x+600=y30x+600=y

4.
d)

2x+250=y2x+250=y

5.
d)

 200−20x=y200-20x=y  

6.
b)

y=5+1.50xy=5+1.50x

7.
b)

5x+35=y5x+35=y

8.
a)

50x+10=y50x+10=y

9.
d) y = x + 4
10.
a) y = 3x + 9
11.
a)

y= 3x+5

12.
a)

t=10d

13.
b)

y = 2x

14.
c)

y = 5x

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FAQs

What does this Writing Equations in 2 Variables worksheet cover?

This Grade 6–8 mathematics worksheet uses 14 multiple-choice questions to help students write or identify two-variable equations. Students translate situations with fixed amounts, rates, costs, increases, and decreases into equations, then match equations to tables and graphs such as y = 2x and y = 5x. Completing these items builds skill in recognizing how constants and multipliers represent relationships between variables.

How can I use this worksheet to teach writing equations in two variables?

Begin by modeling one context item, labeling the starting amount, the per-unit change, the input variable, and the output variable before writing the equation. Then have students explain why the fixed fee is added separately from a per-item or per-hour rate, and use the table and graph questions to connect those equations to visible patterns. Finish with independent completion and a discussion of how an equation such as 200 − 20x represents a decreasing value.

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

Watch for students reversing the fixed amount and rate, such as writing 98x + 45 instead of 98 + 45x, or adding a decrease instead of subtracting it in the Chromebook item. Students may also confuse the coefficient and constant when reading tables and graphs, selecting y = x + 4 instead of the relationship shown or mistaking y = 2x for x = 2y. Ask them to identify what happens when the variable is zero and how much the output changes for each increase in the input.

How do I assign and grade this Writing Equations in 2 Variables worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, with a complete answer key for all 14 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. The printable format also offers an option for schools reducing screen time.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the equation choices, context questions, tables, and graphs are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those changes support access to the algebra practice. These options preserve the worksheet’s multiple-choice format while changing its presentation.

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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