Practice Slope in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A measure of the steepness and direction of a line, calculated as the ratio of vertical change (rise) to horizontal change (run) between any two points on the line. Slope is written as $m = \frac{y_2 - y_1}{x_2 - x_1}$ and indicates how much $y$ changes for each unit increase in $x$ .

How much the line goes up for every step to the right. Steeper = bigger slope.

Showing a random 20 of 50 problems.

Example 1

challenge

Points

A(0, 0)

B(6, 8)

, and

C(c, 0)

form a right triangle with the right angle at

B

. Find

c

Right triangle ABC with right angle at B(6,8) — find c.

Example 2

hard

A line has

x

-intercept

4

and

y

-intercept

-6

. Find its slope.

Find the slope of the line with x-int 4 and y-int −6.

Example 3

medium

Find the slope between

(\tfrac{1}{2}, 3)

and

(\tfrac{5}{2}, 11)

Find the slope through (½,3) and (5/2,11).

Example 4

medium

Convert

6x + 2y = 14

to slope-intercept form.

Example 5

medium

A car's distance after

t

hours is

60t + 20

miles. What does the slope

60

represent?

Example 6

easy

Find the slope of the line through

(1, 2)

and

(4, 8)

Find the slope through A(1,2) and B(4,8).

Example 7

easy

Find the slope of the line

y = 5

Example 8

hard

A pool drains at a steady rate. After

2

minutes it holds

480

gallons; after

7

minutes it holds

355

gallons. What is the slope (gallons per minute)?

Pool draining: find the slope (gallons per minute).

Example 9

medium

Are the lines

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

and

2x - 4y = 7

parallel?

Example 10

medium

Find the slope of the line perpendicular to one with slope

\frac{5}{3}

Example 11

easy

A vertical line has slope equal to what?

Example 12

easy

Find the slope of the line through

(3, 7)

and

(5, 7)

Find the slope through A(3,7) and B(5,7).

Example 13

medium

A line passes through

(1, 4)

and

(3, 10)

. Where does it cross the

y

-axis?

Where does the line through (1,4) and (3,10) cross the y-axis?

Example 14

easy

Find the slope of the line through

(-1, -4)

and

(2, 5)

Find the slope through A(−1,−4) and B(2,5).

Example 15

medium

What's the slope of a wheelchair ramp that rises

2

ft over a

24

-ft run?

Example 16

easy

Find the slope of the line passing through points

(2, 3)

and

(6, 11)

Find the slope of the line through A and B.

Example 17

medium

Find the slope of

2x + 3y = 12

Find the slope of 2x + 3y = 12.

Example 18

medium

Find the slope of the line passing through

(2, 5)

and

(6, 13)

Find the slope through A(2,5) and B(6,13).

Example 19

easy

A ramp rises

3

ft over a

15

ft horizontal run. What is its slope?

Example 20

challenge

Three points

(1, 2)

(4, 8)

(k, 14)

are collinear. Find

k

A(1,2), B(4,8), C(k,14) are collinear. Find k.

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Related Concepts

Coordinate Plane Rates Linear Functions Parallel and Perpendicular