8th Grade Slope and Similar Triangles Test Solutions and Scoring (PDF)

8th Grade math test solutions: Slope and Similar Triangles – Maths PDF

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This slope similar triangles test answers for 8th Grade covers slope and similar triangles (Common Core 8.EE.B.6), with a free PDF to print.

Use this answer key to score the slope and y = mx + b 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.6

Slope similar triangles test answers: worked solutions

Question 1 – Find the slope [2 pts]

\(\frac{9-1}{6-2} = 2\)
\(\frac{-2-4}{3-(-3)} = -1\)

Scoring: 1 point each.

Question 2 – Read an equation [2 pts]

\(m = \frac{2}{3}\), \(b = -5\)
\(2y = -4x + 10\), so \(y = -2x + 5\)

Scoring: 1 point each part.

Question 3 – Equation from a graph [3 pts]

A line.

\(m = \frac{3}{2}\), \(b = -1\).

\(y = \frac{3}{2}x – 1\)

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

Question 4 – Similar triangles [3 pts]

\(\frac{\text{rise}}{12} = \frac{3}{4}\), so rise \(= 9\).

Both are right triangles with the same slope angle, so their angles match.

Scoring: 1 point for setting up the proportion, 1 point for 9, 1 point for the similarity reason.

Question 5 – Two points [3 pts]

Rise 6, run 2.

\(m = \frac{13 – 7}{4 – 2} = 3\).

\(7 = 3 \cdot 2 + b\), so \(b = 1\).

\(y = 3x + 1\)

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

Question 6 – Parallel [2 pts]

Parallel lines have the same slope, \(-2\). The y-intercept is 9.

\(y = -2x + 9\)

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

Question 7 – Streaming [3 pts]

\(y = 9x + 6\).

Slope 9: dollars per month. Intercept 6: the sign-up fee paid at the start.

Scoring: 1 point for the equation. 1 point for each meaning.

Question 8 – Explain [2 pts]

Triangles drawn between different pairs of points are similar, so rise to run is the same ratio each time.

Scoring: 1 point for similar triangles. 1 point for the proportional sides conclusion.

Total score

Total

20 points

Key facts behind this slope similar triangles test answers

Key facts

Slope \(m = \frac{\text{rise}}{\text{run}} = \frac{y_{2} – y_{1}}{x_{2} – x_{1}}\).
Any two points on a line give the same slope because the triangles are similar.
\(y = mx\) goes through the origin; \(y = mx + b\) crosses the y-axis at \((0, b)\).
Parallel lines have equal slopes; horizontal lines have slope 0.
To write an equation, find \(m\), then solve for \(b\) with a point.

How to use this slope similar triangles 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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