8th Grade Proportional Relationships and Slope Test Solutions and Scoring (PDF)

8th Grade math test solutions: Proportional Relationships and Slope – Maths PDF

Cover of the book Grade 8 Math Tests with Answer Keys (PDF)

Download as a PDFThe Grade 8 tests book with answer keysPrintable PDFSee the book ›

Sommaire

This grade 8 proportional relationships test answers for 8th Grade covers proportional relationships and slope (Common Core 8.EE.B.5), with a free PDF to print.

Use this answer key to score the proportional relationships 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.EE.B.5

Grade 8 proportional relationships test answers: worked solutions

Question 1 – Table and rate [2 pts]

$\frac{7}{2} = \frac{14}{4} = \frac{21}{6} = \frac{28}{8} = 3.5$.

$y = 3.5x$

Scoring: 1 point for showing a constant ratio. 1 point for the equation.

Question 2 – Slope from a graph [3 pts]

Rise 5, run 2.

Slope $= \frac{5}{2}$, so $y = \frac{5}{2}x$.

$y = \frac{5}{2} \cdot 10 = 25$.

Scoring: 1 point for the slope, 1 point for the equation, 1 point for 25.

Question 3 – Compare two relationships [3 pts]

A: $\frac{7}{2} = 3.5$. B: 3.

A has the greater rate (3.5 > 3)

Scoring: 1 point for each unit rate. 1 point for the comparison.

Question 4 – Grocery price [2 pts]

$9.40 \div 4 = 2.35$, so $c = 2.35p$.

$2.35 \cdot 7 = 16.45$.

\$16.45

Scoring: 1 point for the equation. 1 point for \$16.45.

Question 5 – Is it proportional? [2 pts]

After 0 months the cost is \$20, not \$0, so the graph would not pass through the origin. The ratio changes: $\frac{30}{1} = 30$ but $\frac{40}{2} = 20$.

Scoring: 1 point for no. 1 point for a valid reason.

Question 6 – Two slopes [2 pts]

Slope triangles.

A: $\frac{3}{4}$. B: $\frac{6}{2} = 3$.

Scoring: 1 point for each slope.

Question 7 – Walking speeds [3 pts]

Ethan: $9 \div 3 = 3$ mph. Maya: 3.2 mph.

Maya, by 0.2 mph

Scoring: 1 point for Ethan’s rate. 1 point for comparing. 1 point for 0.2 mph.

Question 8 – Find the point [3 pts]

$a = \frac{2}{3} \cdot 9 = 6$.

$8 = \frac{2}{3}b$, so $b = 12$.

Scoring: 1 point for the setup. 1 point for $a = 6$. 1 point for $b = 12$.

Total score

Total

20 points

Key facts behind this grade 8 proportional relationships test answers

Key facts

Equation: $y = kx$, where $k = \frac{y}{x}$ is the unit rate.
The graph is a straight line through the origin $(0, 0)$.
Slope = $\frac{\text{rise}}{\text{run}}$, the same between any two points on the line.
A greater unit rate means a steeper line.
In a table, check that $\frac{y}{x}$ is constant.

How to use this grade 8 proportional relationships 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.

Voter.. post

Free printable PDF