Graphing Linear Equations

A linear equation graphs as a straight line.

To graph $y = 2x - 1$:

Plot the points and connect them with a straight line.

X-intercept and Y-intercept

• Y-intercept: Where the line crosses the y-axis ($x = 0$)
• X-intercept: Where the line crosses the x-axis ($y = 0$)

For $y = 2x - 4$:

• Y-intercept: $(0, -4)$
• X-intercept: Set $y = 0$: $0 = 2x - 4 \implies x = 2$, so $(2, 0)$

Horizontal and Vertical Lines

• Horizontal: $y = c$ (example: $y = 3$)
• Vertical: $x = c$ (example: $x = -2$)

Distance on the Coordinate Plane

For horizontal/vertical distances, subtract coordinates:

• Distance from $(1, 3)$ to $(5, 3)$: $|5 - 1| = 4$ units

Practice: Graph $y = -x + 3$ by making a table of values. Find the x-intercept and y-intercept.