Proportional Equations Test Answer Key with Scoring – Grade 7

Question 1 Equation from a Table (2 points)

34 ÷ 4 = 8.5, 85 ÷ 10 = 8.5, 127.5 ÷ 15 = 8.5.

y = 8.5x

Scoring: 1 point for finding k, 1 point for the equation.

Question 2 Equation from a Graph (3 points)

(a) 12 ÷ 5 = 2.4.

(b) y = 2.4x.

(c) 2.4 × 14 = 33.6.

k = 2.4; y = 2.4x; y = 33.6

Scoring: 1 point per part.

Question 3 Smoothie Bar (2 points)

t = 5.25n.

5.25 × 13 = 68.25.

t = 5.25n; $68.25

Scoring: 1 point for the equation, 1 point for the cost.

Question 4 Leaking Tank (3 points)

(a) k = 35 ÷ 4 = 320, so g = 320h.

(b) 320 × 14 = 4220 = 2 110 gallons.

(c) 3 ÷ 320 = 20 hours.

g = 320h; 2 110 gallons; 20 hours

Scoring: 1 point per part.

Question 5 Comparing Gym Plans (3 points)

(a) A: 9.5. B: 30 ÷ 3 = 10, 50 ÷ 5 = 10, 80 ÷ 8 = 10.

(b) Gym A is cheaper per visit.

(c) 20 visits: A costs 190, B costs 200, so B costs $10 more.

$9.50 and $10; Gym A; $10 more

Scoring: 1 point per part.

Question 6 Proportional Equations (2 points)

(a) y = 9x has k = 9. (c) y = x ÷ 9 has k = 19. (b) and (d) are not of the form y = kx.

(a) and (c)

Scoring: 1 point for both correct choices, 1 point for the values of k (0.5 each).

Question 7 Graph Versus Equation (3 points)

(a) 14 ÷ 4 = 3.5, so d = 3.5t.

(b) 3.5 > 3.2, so Jada is faster.

(c) 3.5 × 10 = 35 and 3.2 × 10 = 32, so Jada is 3 miles ahead.

d = 3.5t; Jada; 3 miles

Scoring: 1 point per part.

Question 8 County Sales Tax (2 points)

t = 0.065p.

84 × 0.065 = 5.46.

9.75 ÷ 0.065 = 150.

t = 0.065p; $5.46; $150

Scoring: 1 point for the equation, 0.5 point for each value.