Linear Functions Test Answer Key with Scoring – Grade 8

Question 1 Table to rule (3 points)

1. The outputs rise 6 over a run of 2, so the rate is 3.
2. At x = 0 the output is 14.
3. y = 3x + 14.

(a) 3 (b) 14 (c) y = 3x + 14

Scoring: 1 point per part.

Question 2 Two points (3 points)

1. (8 − (−4)) ÷ (7 − 3) = 12 ÷ 4 = 3.
2. −4 = 3(3) + b = 9 + b, so b = −13.
3. y = 3x − 13. Check (7, 8): 21 − 13 = 8.

(a) 3 (b) −13 (c) y = 3x − 13

Scoring: 1 point per part.

Question 3 Draining a pool (3 points)

1. Rate = (30 − 60) ÷ (10 − 0) = −3 gallons per minute; initial value 60.
2. y = −3x + 60.
3. −3x + 60 = 0 gives x = 20.

(a) −3 and 60 (b) y = −3x + 60 (c) 20 minutes

Scoring: 1 point per part.

Question 4 Trail club fees (3 points)

1. y = 9x + 25.
2. 9(8) + 25 = 97.
3. The rate 9 is the cost of each hike; 25 is the initial value, the membership fee paid before any hike.

(a) y = 9x + 25 (b) $97 (c) $9 per hike and a $25 fee

Scoring: 1 point per part.

Question 5 Hiker’s elevation (3 points)

1. A: elevation increases steadily; a rising line.
2. B: elevation stays the same; a level line, so the hiker is on flat ground or resting.
3. C: elevation decreases steadily; a falling line.

(a) increasing (b) constant (c) decreasing

Scoring: 1 point per section.

Question 6 Sketch a story (2 points)

The graph rises in a straight line, goes level while the kayaker rests, then rises again in a steeper straight line.

Rise, level, steeper rise

Scoring: 1 point for the level rest section, 1 point for a steeper second climb.

Question 7 Drone model (2 points)

Rate = (36 − 12) ÷ (4 − 1) = 8 feet per second. Then 12 = 8(1) + b gives b = 4.

Rate 8; y = 8x + 4

Scoring: 1 point for the rate, 1 point for the function.

Question 8 Linear or not? (1 point)

The outputs change by 3 and then by 5. The rate is not constant, so the function is not linear.

Not linear

Scoring: 1 point for the conclusion with the changes 3 and 5.