8th Grade Slope and Similar Triangles Worksheet Solutions (PDF)

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

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

This answer key gives a full worked solution for each of the 21 problems on the slope and y = mx + b worksheet (Common Core 8.EE.B.6). Compare each step with your own work, not only the final answer, and note any step where your method differed.

Grade 8 · Common Core State Standards: 8.EE.B.6

Slope similar triangles answers: exercises 1 to 10

Exercise 1 – Slope from two points

$m = \frac{8 – 2}{3 – 1} = \frac{6}{2} = 3$.

$3$

Exercise 2 – Negative slope

$m = \frac{-1 – 5}{4 – (-2)} = \frac{-6}{6} = -1$.

$-1$

Exercise 3 – Slope and intercept

Compare with $y = mx + b$.

$m = -3,\ b = 7$

Exercise 4 – Graph it

Values for y = 2x + 1.

Plot the three points and draw the line.

Line through (0, 1), (1, 3), (2, 5)

Exercise 5 – Write the equation

Substitute $m = 4$ and $b = -2$ into $y = mx + b$.

$y = 4x – 2$

Exercise 6 – Equation from a graph

Rise 4 over run 2.

$m = \frac{4}{2} = 2$. The y-intercept is 3.

$y = 2x + 3$

Exercise 7 – Similar triangles

The triangles are similar, so $\frac{\text{rise}}{12} = \frac{2}{3}$.

$\text{rise} = 12 \cdot \frac{2}{3} = 8$.

Both triangles have slope 2/3.

Rise = 8

Exercise 8 – Show equal slopes

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

Both slopes equal $\frac{3}{2}$

Exercise 9 – Equation from two points

$m = \frac{5 – (-1)}{3 – 0} = 2$. The y-intercept is $-1$.

$y = 2x – 1$

Exercise 10 – Find b

$m = \frac{10 – 4}{3 – 1} = 3$.

Use $(1, 4)$: $4 = 3 \cdot 1 + b$, so $b = 1$.

$y = 3x + 1$

Exercises 11 and up

Exercise 11 – Slope and a point

$5 = \frac{1}{2} \cdot 4 + b$, so $5 = 2 + b$ and $b = 3$.

$y = \frac{1}{2}x + 3$

Exercise 12 – Horizontal line

$m = \frac{3 – 3}{5 – (-2)} = 0$. Every point has $y = 3$.

$m = 0,\ y = 3$

Exercise 13 – Rewrite as y = mx + b

Subtract $2x$ from both sides: $y = -2x + 6$.

$m = -2,\ b = 6$

Exercise 14 – Solve for y

Divide every term by 3: $y = 2x – 3$.

$y = 2x – 3$

Exercise 15 – Where it crosses the x-axis

The x-axis has $y = 0$: $0 = 2x – 4$, so $x = 2$.

$(2, 0)$

Exercise 16 – Parallel lines

Both have slope 2, so they are parallel.

Intercepts: 1 and -3, a distance of $1 – (-3) = 4$.

Parallel; 4 units apart

Exercise 17 – Ramp

Slope $= \frac{3}{12} = \frac{1}{4}$.

$\text{rise} = \frac{1}{4} \cdot 20 = 5$.

Slope 1/4; rise 5 feet

Exercise 18 – Taxi fare

Slope 2 (dollars per mile), intercept 3: $y = 2x + 3$.

$y = 2 \cdot 10 + 3 = 23$.

$y = 2x + 3$; \$23

Exercise 19 – Plant growth

$y = 2.5x + 40$.

$y = 2.5 \cdot 12 + 40 = 70$.

$y = 2.5x + 40$; \$70

Exercise 20 – Compare lines

Line A: slope $\frac{4 – 1}{2 – 0} = \frac{3}{2}$, intercept 1.

Line B: slope 1, intercept 5.

A has the greater slope; B has the greater y-intercept

Exercise 21 – Explain

The two right triangles share the same angles, so they are similar and their sides are proportional. $\frac{3}{2}$ and $\frac{6}{4}$ are equal.

Both slopes are $\frac{3}{2}$

Key facts behind this slope similar triangles 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 answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

Download the slope similar triangles answers as a PDF with the button below and keep it with your notes.

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