Grade 8 · Pre-Algebra

Grade 8 Pre-Algebra questions and answers

Ratios, slope, integers, and the Pythagorean theorem. Written in American English for students, parents, and teachers in the United States.

Topics

Practice quiz

Question and answer list

Open a card to see the answer. These are original practice items for US elementary students — not a state test copy.

1. In y = mx + b, m is the

Answer: slope

Rise over run.

2. In y = mx + b, b is the

Answer: y-intercept

The line crosses the y-axis at (0, b).

3. Slope is calculated as

Answer: (y₂ − y₁) / (x₂ − x₁)

Vertical change over horizontal change.

4. A line with slope 0 is

Answer: horizontal

y does not change.

5. A vertical line has

Answer: undefined slope

You would divide by zero.

6. The slope of the line through (1, 2) and (3, 6) is

Answer: 2

(6 − 2) / (3 − 1) = 4/2 = 2.

7. y = −3x + 5 has a slope that is

Answer: negative, so the line falls left to right

Negative m means the line decreases.

8. Parallel lines have

Answer: the same slope

Perpendicular slopes are opposite reciprocals.

9. The Pythagorean theorem is

Answer: a² + b² = c²

Only for right triangles; c is the hypotenuse.

10. The hypotenuse is

Answer: the side opposite the right angle

It is the longest side.

11. If a = 3 and b = 4, c =

Answer: 5

9 + 16 = 25, √25 = 5.

12. If a = 5, b = 12, c =

Answer: 13

25 + 144 = 169, √169 = 13.

13. A 6-8-10 triangle is a

Answer: scaled 3-4-5 right triangle

Multiply 3-4-5 by 2.

14. If c = 10 and a = 6, b =

Answer: 8

36 + b² = 100 → b² = 64.

15. You can use the theorem to find

Answer: the distance between two points on a grid

Think of the legs as Δx and Δy.

16. The theorem does not apply to

Answer: a triangle with no right angle

All angles must include 90°.