Practice Slope in Geometry in Math

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

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 steepness—the ratio of how high it rises to how far it goes horizontally.

Example 1

easy
Find the slope of the line through A(-2, 5) and B(4, -1). Describe what the slope tells us about the line's direction.

Example 2

hard
A road rises 40 metres over a horizontal distance of 500 metres. Express the slope as a percentage grade and as an angle (to the nearest tenth of a degree).

Example 3

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

Example 4

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