Skip to the main content
PeabodyMake a free story

🧩 7th grade math · Patterns & Algebra

Proportional or not?

In a proportional relationship, y ÷ x is always the same number k. It is the constant of proportionality, and y = kx. If y = 10 when x = 4, then k = 10 ÷ 4 = 2.5. For y = 3x, x = 7 gives y = 21, and y = 21 gives x = 21 ÷ 3 = 7.

Worked example

This table shows a proportional relationship.
x: 1, 2, 6, 10
y: 8, 16, 48, 80
What is the constant of proportionality?
Answer: 8
k = y ÷ x = 8 ÷ 1 = 8. So y = 8 × x. Check another pair: 16 ÷ 2 is also 8.

For grown-ups: Unit rates with fractions; recognise proportional relationships (tables, graphs, y = kx). Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 7.RP.A.1–2
What this practises, for teachers

Practices unit rates with fractions; recognise proportional relationships (tables, graphs, y = kx) (7.RP.A.1–2). A printable sheet with its answer key, worked answers on the page, no accounts.

▶ Practise it

For your class

🖨️ Printable sheet and key

Try three

  1. A proportional relationship is y = 2x. What is the constant of proportionality?
    Show the answer and how
    Answer: 2
    In y = kx, the number multiplying x is the constant of proportionality. Here k = 2.
  2. The number of words w a student types in n minutes is w = 4n. How many minutes does the student need to type 28 words?
    Show the answer and how
    Answer: 7 minutes
    Put w = 28 into w = 4n, then divide by 4: 28 ÷ 4 = 7.
  3. In a proportional relationship, y = 84 when x = 7. The relationship is y = kx. What is k, the constant of proportionality?
    Show the answer and how
    Answer: 12
    k = y ÷ x = 84 ÷ 7 = 12. So y = 12 × x.

Before and after

Learn first: Best buy and speed (6th), Change units with ratios (6th)

Comes next: Scale drawings (7th)

Name: ____________________Date: ____________Score: ____ / 12

Proportional or not? (7th grade)

  1. This table shows a proportional relationship.
    x: 6, 12, 18, 24
    y: 36, 72, 108, 144
    What is the constant of proportionality?
  2. This table shows a proportional relationship.
    x: 2, 4, 6, 8
    y: 10, 20, 30, 40
    What is the constant of proportionality?
  3. This table shows a proportional relationship.
    x: 2, 3, 5, 8
    y: 14, 21, 35, 56
    What is the constant of proportionality?
  4. This table shows a proportional relationship.
    x: 3, 4, 6, 10
    y: 6, 8, 12, 20
    What is the constant of proportionality?
  5. In a proportional relationship, y = 5 when x = 1. The relationship is y = kx. What is k, the constant of proportionality?
  6. This table shows a proportional relationship.
    x: 1, 3, 4, 5
    y: 5, 15, 20, 25
    What is the constant of proportionality?
  7. The cost c (in dollars) of p pounds of apples is c = 17.5p. How many pounds of apples can you buy for $105?
  8. The cost c (in dollars) of p pounds of apples is c = 9p. How much do 8 pounds of apples cost?
  9. The distance d (in miles) a car travels in t hours is d = 12.5t. How many hours does the car need to travel 37.5 miles?
  10. This table shows a proportional relationship.
    x: 1, 3, 4, 8
    y: 22, 66, 88, 176
    What is the constant of proportionality?
  11. The distance d (in miles) a car travels in t hours is d = 11t. How many hours does the car need to travel 121 miles?
  12. The number of words w a student types in n minutes is w = 4n. How many minutes does the student need to type 32 words?

Answer key

  1. 6
  2. 5
  3. 7
  4. 2
  5. 5
  6. 5
  7. 6 pounds
  8. $72.00
  9. 3 hours
  10. 22
  11. 11 hours
  12. 8 minutes

More 7th grade skills: all 7th grade math skills, or every grade at math skills.