The **intercepts** of a graph are points at which the graph crosses the axes. The ** x-intercept** is the point at which the graph crosses the

*x-*axis. At this point, the

*y-*coordinate is zero. The

**is the point at which the graph crosses the**

*y-*intercept*y-*axis. At this point, the

*x-*coordinate is zero.

To determine the *x-*intercept, we set *y *equal to zero and solve for *x*. Similarly, to determine the *y-*intercept, we set *x *equal to zero and solve for *y*. For example, lets find the intercepts of the equation [latex]y=3x - 1[/latex].

To find the *x-*intercept, set [latex]y=0[/latex].

To find the *y-*intercept, set [latex]x=0[/latex].

We can confirm that our results make sense by observing a graph of the equation as in Figure 10. Notice that the graph crosses the axes where we predicted it would.

### How To: Given an equation, find the intercepts.

- Find the
*x*-intercept by setting [latex]y=0[/latex] and solving for [latex]x[/latex]. - Find the
*y-*intercept by setting [latex]x=0[/latex] and solving for [latex]y[/latex].

### Example 4: Finding the Intercepts of the Given Equation

Find the intercepts of the equation [latex]y=-3x - 4[/latex]. Then sketch the graph using only the intercepts.

### Solution

Set [latex]y=0[/latex] to find the *x-*intercept.

Set [latex]x=0[/latex] to find the *y-*intercept.

Plot both points, and draw a line passing through them as in Figure 11.

### Try It 1

Find the intercepts of the equation and sketch the graph: [latex]y=-\frac{3}{4}x+3[/latex].