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7th grade · Math · Unit 14 of 20

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.

New York State Learning Standards learning standard: NY-7.RP.1; NY-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 New York

In the New York State Learning Standards, this is unit 14 of 20 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: New York State Education Department (NYSED)

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

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

    xy
    228
    456
    684
    • 14
    • 16
    • 28
    • 11

  2. Question 2

    Leo walks 1/2 mile in 1/4 hour. What is the unit rate in miles per hour?

    • 3 miles per hour
    • 1/2 miles per hour
    • 1/8 miles per hour
    • 2 miles per hour

  3. Question 3

    y is proportional to x, and y = 54 when x = 9. Which equation fits?

    • y = 6x
    • y = 54x
    • y = 9x
    • y = x + 45

  4. Question 4

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

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

  5. Question 5

    Does the table show a proportional relationship?

    xy
    214
    535
    856
    • No, y ÷ x is not the same for every pair
    • Yes, y ÷ x is always 7

  6. Question 6

    y is proportional to x, and y = 12 when x = 6. Which equation fits?

    • y = 12x
    • y = x + 6
    • y = 6x
    • y = 2x

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