7th grade · Math · Unit 14 of 15
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.
Minnesota K-12 Academic Standards benchmark: 7.3.7.2; 7.3.7.3; 7.3.5.7 · unit rates and recognizing proportional relationships
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 Minnesota
In the Minnesota K-12 Academic Standards, this is unit 14 of 15 in 7th grade Math, after Multiply & Divide Signed Numbers and before Scale Drawings.
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.
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
y is proportional to x, and y = 20 when x = 2. Which equation fits?
- y = 2x
- y = 20x
- y = x + 18
- y = 10x
y = 10x
Hint: k = y ÷ x = 20 ÷ 2 = 10.
Question 2
The graph of a proportional relationship passes through (1, 7). What does 7 tell you?
- The total of x and y
- 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 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 3
Does the table show a proportional relationship?
x y 1 11 4 29 6 41 - No, y ÷ x is not the same for every pair
- Yes, y ÷ x is always 6
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
Ravi reads 2/3 page in 1/3 minute. What is the unit rate in pages per minute?
- 3 pages per minute
- 2 pages per minute
- 1/2 pages per minute
- 2/9 pages per minute
2 pages per minute
Hint: Divide: 2/3 ÷ 1/3 = 2.
Question 5
What is the constant of proportionality (y ÷ x) in the table?
x y 3 36 5 60 6 72 - 12
- 15
- 36
- 14
12
Hint: 36 ÷ 3 = 12.
Question 6
What is the constant of proportionality (y ÷ x) in the table?
x y 3 30 4 40 5 50 - 10
- 30
- 13
- 7
10
Hint: 30 ÷ 3 = 10.