Slope and Proportional Relationships Test Answer Key with Scoring – Grade 8

Question 1 Proportional table (3 points)

1. 10.5 ÷ 3 = 3.5, 17.5 ÷ 5 = 3.5 and 31.5 ÷ 9 = 3.5. The ratio is constant, so yes.
2. k = 3.5.
3. y = 3.5x.

(a) Yes (b) 3.5 (c) y = 3.5x

Scoring: 1 point per part.

Question 2 Slope of a line (3 points)

(a) Rise = −12 − 4 = −16 and run = 5 − (−3) = 8, so the slope is −16 ÷ 8 = −2.

(b) The slope is negative, so the line falls.

(a) −2 (b) falls

Scoring: (a) 1 point for the rise and run, 1 point for −2. (b) 1 point.

Question 3 Grapes at two stands (3 points)

1. Slope = 7 ÷ 5 = 1.4 dollars per pound.
2. 1.55 dollars per pound.
3. 1.40 < 1.55, so Stand A is cheaper by $0.15 per pound.

(a) $1.40 (b) $1.55 (c) Stand A

Scoring: 1 point per part.

Question 4 Two slope triangles (3 points)

1. 4 ÷ 6 = 23.
2. 10 ÷ 15 = 23.
3. The triangles share an angle at the origin and each has a right angle, so they are similar. Matching sides are in equal ratios, so rise ÷ run is the same.

Both slopes are 23.

Scoring: 1 point per part.

Question 5 Slope and intercept (2 points)

Compare with y = mx + b: m = −58 and b = 9.

Slope −58; y-intercept 9

Scoring: 1 point each.

Question 6 Proportional equation (2 points)

k = 9 ÷ 12 = 34, so y = 34x. When x = 20: 34 · 20 = 15.

y = 34x; y = 15

Scoring: 1 point for the equation, 1 point for 15.

Question 7 Plumber’s fee (3 points)

1. y = 38x + 45.
2. 38 · 3.5 = 133, and 133 + 45 = 178.
3. No. At 0 hours the cost is $45, so the graph does not pass through the origin.

(a) y = 38x + 45 (b) $178 (c) Not proportional

Scoring: 1 point per part.

Question 8 Flat line (1 point)

It is a horizontal line through (0, 4). The rise is always 0, so the slope is 0.

Horizontal line; slope 0

Scoring: 1 point for slope 0 with a description.