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Graphing proportional relationships worksheet

Grade 7 math, Common Core 7.RP.A.2. 6 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

By the StudyWiz teamUpdated October 23, 2026How we write our pages

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Graphing proportional relationships

Grade 7 math, Common Core 7.RP.A.2

Use each graph or equation to answer the questions.

  1. 1.
    The graph shows miles for hours. What is the unit rate?
    0123456051015202530hoursmiles
  2. 2.
    Is the relationship in the graph proportional? Explain.
    0123456024681012pounds of grapescost (dollars)
  3. 3.
    What does the point (3, 6) on the graph mean? What is the unit rate?
    0123456024681012dayspages read
  4. 4.
    Is the relationship in the graph proportional? Explain.
    01234560369121518hoursmiles
  5. 5.
    The graph of a proportional relationship passes through (2, 6). What is y when x = 1? When x = 8?
  6. 6.
    The graph of a proportional relationship passes through (6, 18). What is y when x = 1? When x = 8?
Free worksheets for grades 6 to 8 from StudyWiz, with answer keys: studywiz.online/worksheets

Answer key: Graphing proportional relationships

Grade 7 math. Each answer has a few worked steps, to help check the method as well as the answer.

  1. 1. 5 miles per hour

    The line passes through (1, 5)

  2. 2. Yes. It is a straight line through (0, 0).

  3. 3. 6 pages are read in 3 days. The unit rate is 2 pages per day.

    6 ÷ 3 = 2

  4. 4. No. The line is straight, but it crosses the y-axis at 6, not at (0, 0).

  5. 5. 3; 24

    k = 6 ÷ 2 = 33 × 8 = 24

  6. 6. 3; 24

    k = 18 ÷ 6 = 33 × 8 = 24

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About graphing proportional relationships

The graph of a proportional relationship is a straight line through the origin, (0, 0). The point (1, r) on the line shows the unit rate r, and any point (x, y) on it gives the constant of proportionality as y ÷ x. A line that doesn’t pass through the origin is not proportional, even if it is straight.

Worked example 1

The graph shows cost (dollars) for pounds of grapes. What is the unit rate?
012345604812162024pounds of grapescost (dollars)
  1. Step 1.The line passes through (1, 4)

Answer: 4 dollars per pound

Worked example 2

What does the point (3, 9) on the graph mean? What is the unit rate?
01234560369121518hoursmiles
  1. Step 1.9 ÷ 3 = 3

Answer: 9 miles are covered in 3 hours. The unit rate is 3 miles per hour.

Worked example 3

The graph of a proportional relationship passes through (2, 6). What is y when x = 1? When x = 10?
  1. Step 1.k = 6 ÷ 2 = 3
  2. Step 2.3 × 10 = 30

Answer: 3; 30

Watch out for

  • Check two things: is it a straight line, and does it go through (0, 0)?
  • Read the y-value where x = 1 to get the unit rate.
  • Pick a point where the line crosses grid lines exactly, so you can read it accurately.

Practice graphing proportional relationships online

On StudyWiz, your kid can practice graphing proportional relationships with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

More grade 7 math worksheets

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