Line of Best Fit Test Answer Key with Scoring – Grade 8

Question 1 Use a model (2 points)

(a) 6 · 9 + 14 = 68

(b) 6x + 14 = 104, so 6x = 90 and x = 15

Scoring: 1 point per part.

Question 2 Read a trend line (3 points)

(a) The line passes through (0, 6) and (10, 36). Slope: (36 − 6) ÷ 10 = 3; intercept: 6.

(b) y = 3x + 6

(c) 3 · 14 + 6 = 48 meters

Scoring: 1 point per part.

Question 3 Meaning in context (3 points)

(a) The tank loses 2.5 gallons each minute.

(b) The tank starts with 90 gallons.

(c) −2.5x + 90 = 0, so x = 90 ÷ 2.5 = 36 minutes.

Scoring: 1 point per part.

Question 4 Choose the better line (3 points)

(a) Line A

(b) Line A passes close to every point and has points on both sides. Line B starts above the points on the left and falls below them on the right, so it misses the trend (its slope 0.5 is much smaller than the rise of the data).

Scoring: part (a) 1 point; part (b) 1 point per valid reason.

Question 5 Equation from two points (3 points)

(a) (43 − 19) ÷ (8 − 2) = 24 ÷ 6 = 4

(b) 19 = 4 · 2 + b, so b = 11: y = 4x + 11

(c) 4 · 12 + 11 = 59

Scoring: 1 point per part.

Question 6 Trusting a prediction (2 points)

The line is based on ages from 0 to 12 months. Ten years is far outside that range, and growth slows down, so the straight-line trend does not continue.

This is extrapolation far beyond the data; 140 inches is unrealistic

Scoring: 1 point for naming extrapolation, 1 point for a reason.

Question 7 Bracelet sales (2 points)

(a) About 1.5 bracelets are sold each day.

(b) 1.5 · 20 + 8 = 38 bracelets

Scoring: 1 point per part.

Question 8 Candle burning (2 points)

−0.75x + 18 = 6, so −0.75x = −12.

x = 12 ÷ 0.75 = 16.

After 16 hours

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