Subscribe

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.

Alaska 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

Proportional Relationships in Alaska

In the Alaska content standards, this is unit 14 of 17 in 7th grade Math, after Multiply & Divide Signed Numbers and before Angle Relationships.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Alaska Department of Education and Early Development

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
    29
    311
    617
    • No, y ÷ x is not the same for every pair
    • Yes, y ÷ x is always 2

  2. Question 2

    The graph of a proportional relationship passes through (1, 5). What does 5 tell you?

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

  3. Question 3

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

    xy
    24
    48
    612
    • 2
    • 4
    • 1
    • 5

  4. Question 4

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

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

  5. Question 5

    y is proportional to x, and y = 36 when x = 4. Which equation fits?

    • y = 9x
    • y = 36x
    • y = 4x
    • y = x + 32

  6. Question 6

    The graph of a proportional relationship passes through (1, 3). What does 3 tell you?

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

More 7th grade