Linear Equations
8-3Slope of a Line
Overview
Slope m = (y₂ − y₁) / (x₂ − x₁): rise over run. Measures steepness and direction.
Key ideas
- Positive slope: line rises left-to-right.
- Negative slope: line falls.
- Horizontal lines have slope 0; vertical lines have undefined slope.
Worked examples
Example 1
Problem. Slope through (1, 2) and (4, 8)?
Solution. (8 − 2)/(4 − 1) = 6/3 = 2.
Practice
Try each one. Click Show answer when ready.
- 1.
Slope through (0,0) and (5, 10).
- 2.
Slope through (3, 4) and (3, 9).
- 3.
Slope through (−2, 5) and (2, −3).
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Find the slope of the line through (4, −1) and (−2, 5).
- 2.
A line has slope 2/3. If x increases by 6, how much does y increase?