Lesson 17: Slope-Intercept Form
The slope-intercept form of a linear equation is written as:
y = mx + b
- m = slope of the line
- b = y-intercept (where the line crosses the y-axis)
This form makes it easy to graph a line: start at the y-intercept and use the slope to find another point.
Examples
Example 1: Graph \(y = 2x + 1\)
- y-intercept: b = 1 → plot point (0,1)
- Slope: m = 2 → rise 2, run 1 → next point (1,3)
Example 2: Graph \(y = -\frac{1}{2}x + 4\)
- y-intercept: b = 4 → plot point (0,4)
- Slope: m = -1/2 → down 1, right 2 → next point (2,3)
Practice Problems
- Graph \(y = 3x - 2\)
- Graph \(y = -x + 5\)
- Write the slope-intercept form of the line passing through (0,2) with slope 4
- Write the slope-intercept form of the line passing through (1,3) with slope -2
Lesson Summary
- Slope-intercept form: y = mx + b
- m = slope, b = y-intercept
- To graph: plot y-intercept, then use slope to find a second point