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7th grade · Math · Unit 14 of 17

Proportional Relationships

y = kx

What your child practices

Deciding whether a table shows a proportional relationship, finding the constant of proportionality, writing y = kx, and unit rates with fractions.

California Content Standards learning standard: 7.RP.1; 7.RP.2 · unit rates with fractions, recognizing proportional relationships and finding the constant of proportionality

How we explain it

Children can open this short lesson before they practice.

  1. In a proportional relationship, y ÷ x is the same for every pair.
  2. That ratio is the constant of proportionality, k.
  3. The equation is y = kx.

Example: x = 2, y = 10 and x = 5, y = 25. What is k? 10 ÷ 2 = 5 and 25 ÷ 5 = 5. Answer: k = 5

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    Does the table show a proportional relationship?

    xy
    520
    832
    1040
    • Yes, y ÷ x is always 4
    • No, y ÷ x is not the same for every pair

  2. Question 2

    The graph of a proportional relationship passes through (1, 11). What does 11 tell you?

    • Where the line starts on the y-axis
    • The total of x and y
    • How many points are on the graph
    • The unit rate: y for each 1 of x

  3. Question 3

    Mia walks 3/4 mile in 1/4 hour. What is the unit rate in miles per hour?

    • 3 miles per hour
    • 1/3 miles per hour
    • 3/16 miles per hour
    • 4 miles per hour

  4. Question 4

    What is the constant of proportionality (y ÷ x) in the table?

    xy
    224
    672
    896
    • 24
    • 10
    • 14
    • 12

  5. Question 5

    y is proportional to x, and y = 40 when x = 5. Which equation fits?

    • y = 40x
    • y = 5x
    • y = 8x
    • y = x + 35

  6. Question 6

    Sam uses 3/4 cup of flour for 1/2 batch. What is the unit rate in cups per batch?

    • 2/3 cups per batch
    • 3/8 cups per batch
    • 2 1/2 cups per batch
    • 1 1/2 cups per batch

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