Lesson 5: Slope and Intercepts

Property

The intercepts of a line are the points where the graph crosses the axes. Because the $y$-intercept of a graph lies on the $y$-axis, its $x$-coordinate must be zero. And because the $x$-intercept lies on the $x$-axis, its $y$-coordinate must be zero.

Examples

• A line crosses the x-axis at $(5, 0)$ and the y-axis at $(0, -2)$. The x-intercept is $(5, 0)$ and the y-intercept is $(0, -2)$.

• For the line $y = x + 3$, the graph intersects the y-axis at $(0, 3)$ and the x-axis at $(-3, 0)$. These are its intercepts.

Property

To graph a line using intercepts: find the x-intercept by setting $y = 0$, find the y-intercept by setting $x = 0$, plot both intercept points, then draw a straight line through them.

Examples

Property

The slope-intercept form of an equation of a line with slope $m$ and y-intercept, $(0, b)$, is

Examples

• Identify the slope and y-intercept for the line $y = -2x + 8$. The equation is in $y=mx+b$ form. The slope $m$ is $-2$, and the y-intercept is at $(0, 8)$.

• For the equation $3x + y = 7$, first solve for $y$ to get $y = -3x + 7$. Now you can see the slope $m$ is $-3$ and the y-intercept is at $(0, 7)$.