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.
Maine Learning Results learning standard: 7.RP.A.1; 7.RP.A.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.
- In a proportional relationship, y ÷ x is the same for every pair.
- That ratio is the constant of proportionality, k.
- 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 Maine
In the Maine Learning Results, 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: Maine Department of Education
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
The graph of a proportional relationship passes through (1, 12). What does 12 tell you?
- How many points are on the graph
- The unit rate: y for each 1 of x
- The total of x and y
- Where the line starts on the y-axis
The unit rate: y for each 1 of x
Hint: At x = 1, the y-value is the amount per one unit: the unit rate.
Question 2
What is the constant of proportionality (y ÷ x) in the table?
x y 3 36 4 48 6 72 - 36
- 11
- 12
- 15
12
Hint: 36 ÷ 3 = 12.
Question 3
Does the table show a proportional relationship?
x y 2 21 3 29 10 85 - No, y ÷ x is not the same for every pair
- Yes, y ÷ x is always 8
No, y ÷ x is not the same for every pair
Hint: Divide y by x for each row. In a proportional relationship the ratio is always the same.
Question 4
Jay walks 5/8 mile in 1/4 hour. What is the unit rate in miles per hour?
- 2 1/2 miles per hour
- 3 1/2 miles per hour
- 5/32 miles per hour
- 2/5 miles per hour
2 1/2 miles per hour
Hint: Divide: 5/8 ÷ 1/4 = 2 1/2.
Question 5
y is proportional to x, and y = 56 when x = 8. Which equation fits?
- y = 56x
- y = x + 48
- y = 8x
- y = 7x
y = 7x
Hint: k = y ÷ x = 56 ÷ 8 = 7.
Question 6
The graph of a proportional relationship passes through (1, 7). What does 7 tell you?
- The unit rate: y for each 1 of x
- How many points are on the graph
- Where the line starts on the y-axis
- The total of x and y
The unit rate: y for each 1 of x
Hint: At x = 1, the y-value is the amount per one unit: the unit rate.