Lesson 16: Slope of a Line
The slope of a line measures its steepness and direction. It tells us how much the line rises or falls for each unit it moves horizontally.
Slope is often denoted by m and can be positive, negative, zero, or undefined.
Slope Formula
If a line passes through two points \((x_1, y_1)\) and \((x_2, y_2)\), the slope is:
m = (yâ‚‚ - yâ‚) / (xâ‚‚ - xâ‚)
This formula calculates "rise over run": the change in y divided by the change in x.
Example
Find the slope of the line passing through (2, 3) and (5, 11):
- yâ‚‚ - yâ‚ = 11 - 3 = 8
- xâ‚‚ - xâ‚ = 5 - 2 = 3
- Slope: m = 8 / 3
Practice Problems
- Find the slope of the line through (1,2) and (4,8).
- Find the slope of the line through (-2,5) and (3,-10).
- Graph the line with slope 2 and y-intercept 1.
- Graph the line through points (0,0) and (3,6).
Lesson Summary
- Slope measures the steepness and direction of a line.
- Formula: m = (yâ‚‚ - yâ‚) / (xâ‚‚ - xâ‚).
- Positive slope → line rises; negative slope → line falls.
- Zero slope → horizontal line; undefined slope → vertical line.