What is the Graph of a Linear Equation?
The graph of a linear equation in two variables is the set of all points (x, y) whose coordinates satisfy the equation. This graph is always a straight line.
Steps to Graph a Linear Equation:
- Find at least three solutions (ordered pairs) of the equation
- Plot these points on the Cartesian plane
- Draw a straight line passing through all plotted points
- Extend the line in both directions with arrows
Why Three Points?
Two points determine a line, but using a third point helps verify accuracy — all three should be collinear (lie on the same line).
Graphing Special Cases:
| Equation Type | Example | Graph Description |
|---|---|---|
| y = constant | y = -2 | Horizontal line through (0, -2) |
| Through origin | y = 2x | Line passing through (0, 0) |
| ax + by = 0 | 2x + y = 0 | Line through origin |
Intercepts Method:
- x-intercept: Point where line crosses x-axis (y = 0)
- y-intercept: Point where line crosses y-axis (x = 0)