8th Grade Linear Functions as Models Test Solutions and Scoring (PDF)

8th Grade math test solutions: Linear Functions as Models – Maths PDF

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This linear function models test answers for 8th Grade covers linear functions as models (Common Core 8.F.B.4, 8.F.B.5), with a free PDF to print.

Use this answer key to score the linear function models test out of 20 points. Each solution shows the full work and a scoring guide, so partial credit can be given fairly when a student shows correct steps but makes an arithmetic slip.

Grade 8 · Common Core State Standards: 8.F.B.4, 8.F.B.5

Linear function models test answers: worked solutions

Question 1 – Rate and initial value [3 pts]

Rise 9, run 3.

Rate \(\frac{13 – 4}{3} = 3\); initial value 4.

\(y = 3x + 4\)

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

Question 2 – Two points [3 pts]

\(m = 3\). \(8 = 3 \cdot 1 + b\), so \(b = 5\).

\(y = 3x + 5\)

Scoring: 1 point for the slope, 1 point for \(b\), 1 point for the equation.

Question 3 – Interpret [2 pts]

8: dollars for each student. 40: a fixed cost that is paid no matter how many students go.

Scoring: 1 point for each meaning.

Question 4 – Describe a graph [3 pts]

Three parts.

0 to 2 minutes: increasing. 2 to 4 minutes: constant. 4 to 6 minutes: decreasing.

Scoring: 1 point for each part.

Question 5 – Model and predict [3 pts]

\(c = 60 – 3m\); \(c(12) = 24\).

Scoring: 1 point for the rate, 1 point for the function, 1 point for 24%.

Question 6 – Table [2 pts]

The rate is 3 each time. \(11 = 3 \cdot 2 + b\), so \(b = 5\): \(y = 3x + 5\).

Scoring: 1 point for linear with constant rate. 1 point for the equation.

Question 7 – Compare [2 pts]

A: \(6 \cdot 12 + 20 = 92\). B: \(4 \cdot 12 + 35 = 83\).

Plan B

Scoring: 1 point for each total, or 1 for both and 1 for the answer.

Question 8 – Linear or not [2 pts]

No. The graph is curved, so the rate of change is not constant: it gets steeper as x increases.

Scoring: 1 point for nonlinear. 1 point for the reason.

Total score

Total

20 points

Key facts behind this linear function models test answers

Key facts

Rate of change \(m = \frac{\text{change in } y}{\text{change in } x}\); initial value \(b\) is \(y\) when \(x = 0\).
Build a model: find \(m\), solve for \(b\) with one point, write \(y = mx + b\).
A negative rate means the quantity decreases.
A flat segment has rate 0; a curve means the rate is not constant.
Always say what \(m\) and \(b\) mean in the situation, with units.

How to use this linear function models test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All Grade 8 chapters: Grade 8 math.

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