7th grade · Math · Unit 5 of 22
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.
Texas Essential Knowledge and Skills (TEKS) teks student expectation: 7.4(A); 7.4(B); 7.4(C) · constant rates, unit rates and 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 Texas
In the Texas Essential Knowledge and Skills (TEKS), this is unit 5 of 22 in 7th grade Math, after Decimal Operations and before Percents & Proportions.
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: Texas Education Agency (TEA)
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
Noah swims 1/3 lap in 1/6 minute. What is the unit rate in laps per minute?
- 1/18 laps per minute
- 1/2 laps per minute
- 2 laps per minute
- 3 laps per minute
2 laps per minute
Hint: Divide: 1/3 ÷ 1/6 = 2.
Question 2
y is proportional to x, and y = 99 when x = 9. Which equation fits?
- y = 11x
- y = x + 90
- y = 9x
- y = 99x
y = 11x
Hint: k = y ÷ x = 99 ÷ 9 = 11.
Question 3
Does the table show a proportional relationship?
x y 2 6 5 15 10 30 - Yes, y ÷ x is always 3
- No, y ÷ x is not the same for every pair
Yes, y ÷ x is always 3
Hint: Divide y by x for each row. In a proportional relationship the ratio is always the same.
Question 4
What is the constant of proportionality (y ÷ x) in the table?
x y 2 28 4 56 6 84 - 17
- 16
- 14
- 28
14
Hint: 28 ÷ 2 = 14.
Question 5
The graph of a proportional relationship passes through (1, 10). What does 10 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 6
What is the constant of proportionality (y ÷ x) in the table?
x y 3 30 4 40 6 60 - 10
- 13
- 30
- 12
10
Hint: 30 ÷ 3 = 10.