7th grade · Math · Unit 14 of 18
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.
Alabama Course of Study content standard: 7.1; 7.2 · unit rates with fractions 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 Alabama
In the Alabama Course of Study, this is unit 14 of 18 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.
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
What is the constant of proportionality (y ÷ x) in the table?
x y 4 60 5 75 8 120 - 19
- 14
- 60
- 15
15
Hint: 60 ÷ 4 = 15.
Question 2
Ana walks 1/2 mile in 1/4 hour. What is the unit rate in miles per hour?
- 1/8 miles per hour
- 1/2 miles per hour
- 2 miles per hour
- 3 miles per hour
2 miles per hour
Hint: Divide: 1/2 ÷ 1/4 = 2.
Question 3
y is proportional to x, and y = 18 when x = 3. Which equation fits?
- y = 3x
- y = 6x
- y = x + 15
- y = 18x
y = 6x
Hint: k = y ÷ x = 18 ÷ 3 = 6.
Question 4
The graph of a proportional relationship passes through (1, 12). What does 12 tell you?
- The unit rate: y for each 1 of x
- Where the line starts on the y-axis
- The total of x and y
- How many points are on the graph
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 5
Does the table show a proportional relationship?
x y 4 19 6 27 8 35 - Yes, y ÷ x is always 4
- No, y ÷ x is not the same for every pair
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 6
Does the table show a proportional relationship?
x y 4 12 5 14 8 20 - No, y ÷ x is not the same for every pair
- Yes, y ÷ x is always 2
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.