Practice Slope in Geometry in Math

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

Worksheet PDF Free Answer-key PDF Family

Quick Recap

The steepness of a line expressed as rise over run, connecting the algebraic slope formula to the geometric angle of inclination.

A ramp's steepnessβ€”the ratio of how high it rises to how far it goes horizontally.

Showing a random 20 of 50 problems.

Example 1

easy
A slope of 1 corresponds to what angle with the horizontal?

Example 2

easy
Why is the slope of a vertical line undefined?

Example 3

challenge
Explain why slope is the same between ANY two points on a given line, and why this fails for a curve.

Example 4

challenge
A line through (2,3)(2, 3) with negative slope mm cuts off a triangle from the first quadrant with the coordinate axes. Find the slope mm that minimizes the length of the segment between the two axis intercepts.

Example 5

challenge
A line through the origin has inclination angle θ\theta such that the line passes through (4,3)(4, 3). Find tan⁑θ\tan\theta and sin⁑θ\sin\theta.

Example 6

easy
A line goes down from left to right. Is its slope positive or negative?

Example 7

easy
What is the slope of a horizontal line?

Example 8

easy
Which of these lines is steeper: y=5x+2y = 5x + 2 or y=βˆ’7xβˆ’3y = -7x - 3? Which has a greater angle with the xx-axis?

Example 9

easy
A wheelchair ramp rises 0.50.5 m over a run of 66 m. What is its slope?

Example 10

medium
A line has slope βˆ’34-\tfrac{3}{4}. If it rises (changes yy) by βˆ’6-6, what is the change in xx?

Example 11

medium
Find the slope of the line that is perpendicular to 2xβˆ’5y=102x - 5y = 10.

Example 12

hard
Slope of the line through (a,a2)(a, a^2) and (b,b2)(b, b^2) on the parabola y=x2y = x^2 equals ___ (in terms of aa and bb).

Example 13

easy
Find the slope of the line through (βˆ’5,2)(-5, 2) and (3,βˆ’2)(3, -2).

Example 14

hard
A treadmill is inclined at 7.5%7.5\% grade. What is the angle of incline to the nearest tenth of a degree?

Example 15

medium
The median rent in a city rose from $1,200 in 2018 to $1,560 in 2022. Treating year as xx and rent as yy, find the slope (units $/year).

Example 16

medium
Points A(1,2)A(1, 2), B(4,k)B(4, k), C(7,14)C(7, 14) are collinear. Find kk.

Example 17

easy
If a line passes through (0,4)(0, 4) and (5,4)(5, 4), its slope is ___.

Example 18

hard
Find the slope of the line tangent to the circle x2+y2=25x^2 + y^2 = 25 at the point (3,4)(3, 4).

Example 19

medium
Why does a constant slope mean the line is straight?

Example 20

easy
What is the slope of a vertical line?
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