Proportional Relationships Test Answer Key with Scoring – Grade 7

Question 1 Is the Table Proportional (2 points)

12 ÷ 5 = 2.4, 19.2 ÷ 8 = 2.4, 28.8 ÷ 12 = 2.4.

Proportional; k = 2.4

Scoring: 1 point for computing all three ratios, 1 point for the conclusion and k.

Question 2 Not Proportional Table (2 points)

6 ÷ 1 = 6, 11 ÷ 2 = 5.5, 16 ÷ 3 ≈ 5.33, 26 ÷ 5 = 5.2.

Not proportional, because the ratios are not equal

Scoring: 1 point for computing at least two different ratios, 1 point for the conclusion.

Question 3 Reading a Graph (3 points)

(a) The graph is a straight line through (0, 0), so it is proportional.

(b) 9 ÷ 4 = 2.25 and 18 ÷ 8 = 2.25, so k = 2.25.

(c) Working 0 hours earns $0.

Proportional; k = 2.25; 0 hours earn $0

Scoring: 1 point per part.

Question 4 Explain the Error (2 points)

The line crosses the y-axis at (0, 2), so it does not contain (0, 0).

Ratios: 5 ÷ 3 ≈ 1.67 and 8 ÷ 6 ≈ 1.33 are not equal.

Liam is wrong: the line does not pass through the origin

Scoring: 1 point for noting it misses (0, 0), 1 point for supporting evidence.

Question 5 Copy Shop (3 points)

(a) k = 0.09 dollars per page, the cost of 1 page.

(b) 250 × 0.09 = 22.50.

(c) Yes: 0 pages cost $0.

k = 0.09; $22.50; yes

Scoring: 1 point per part.

Question 6 Three Situations (3 points)

(a) Proportional: cost = 12 × hours, so 0 hours cost $0.

(b) Not proportional: at 0 weeks the height is 5 inches, not 0.

(c) Proportional: distance = 48 × hours, a constant ratio.

(a) yes, (b) no, (c) yes

Scoring: 1 point per part (0.5 for the answer, 0.5 for the reason).

Question 7 Hours and Miles with Fractions (3 points)

(a) 94 ÷ 34 = 3, 92 ÷ 32 = 3, 12 ÷ 4 = 3, so k = 3 miles per hour.

(b) 3 × 6 12 = 19 12 miles.

(c) 15 ÷ 3 = 5 hours.

Proportional; 19 12 miles; 5 hours

Scoring: 1 point per part.

Question 8 Finding Missing Values (2 points)

k = 15 ÷ 6 = 2.5.

y = 2.5 × 10 = 25.

k = 2.5; y = 25

Scoring: 1 point for k, 1 point for y.