Lesson 15: Graphing Linear Equations
A linear equation is an equation that creates a straight line when graphed. It can often be written in the form \(y = mx + b\), where:
- \(m\) is the slope (rise over run)
- \(b\) is the y-intercept (where the line crosses the y-axis)
Steps to Graph a Linear Equation
- Identify the slope \(m\) and y-intercept \(b\) from the equation.
- Plot the y-intercept on the y-axis.
- Use the slope to find another point (rise over run from the y-intercept).
- Draw a straight line through the points.
Example: Graph \(y = 2x + 1\)
- y-intercept: \(b = 1\) → plot point (0,1)
- Slope: \(m = 2\) → rise 2, run 1 → next point (1,3)
- Draw a line through (0,1) and (1,3)
Practice Problems
- Graph \(y = -x + 2\)
- Graph \(y = \frac{1}{2}x - 1\)
- Graph \(y = 3\)
- Graph \(y = -2x - 3\)
Lesson Summary
- Linear equations produce straight lines.
- Graph using the y-intercept and slope.
- Check multiple points to ensure accuracy.