The **intercepts** of a linear equation are the places where the axes catch the pass thrown by the linear equation. This is our effort to make linear equations seem remotely athletic. In reality, they have about as much physical ability as Tim Tebow. Oh, snap.

(Shmoop is strongly partisan about football, in case you couldn't tell.)

In non-sports-analogy terms, the intercepts are the spots at which the axes and the graph of the linear equation overlap one another. The *x*-intercept is the place where the graph hits the *x*-axis, and the *y*-intercept is the place where the graph hits the *y*-axis. It would be awfully confusing if it were the other way around.

A linear equation may have one or two intercepts. Sometimes either the *x*-intercept or the *y*-intercept doesn't exist, or so intercept atheists would have you believe.

Knowing both intercepts for a linear equation is enough information to draw the graph, provided the intercepts are not 0. If they are 0, then our graph could be drawn any which way.

### Sample Problems

Draw the graph of the linear equation with *x*-intercept 3 and *y*-intercept 4.

First we draw points at the intercepts:

Then we connect the dots:

If the graph goes through the origin (0, 0), then both of the intercepts are 0 and we don't have enough information to draw the graph. We even tried calling 411, but they acted as if they had no idea what we were talking about.

Our graph could look like this:

## Intercepts Practice:

Find the intercepts for the following graph.
| |

The *x*-intercept is *x* = 1, and the *y*-intercept is *y* = 3. | |

Find the intercepts for the following graph. | |

The *x*-intercept is *x* = 2. Since the graph never hits the *y*-axis, the *y*-intercept does not exist. | |

Draw the graph of the linear equation with *y*-intercept 2 and no *x*-intercept. Clearly, the *x*-axis would have a higher quarterback rating in this scenario. There we go, back to the football. | |

First we draw the intercept: For a line to go through this point and never hit the *x*-axis, the line must be horizontal, and therefore parallel to the *x*-axis. Remember how parallel lines never touch each other? It's not just because they are intense germophobes either. | |

Find the intercepts for the following graph.

Answer

The *x*-intercept is *x* = -1, and the *y*-intercept is *y* = 4.

Find the intercepts for the following graph.

Answer

The *x*-intercept is *x* = 2 and the *y*-intercept is *y* = -4.

Find the intercepts for the following graph.

Answer

The *x*-intercept is *x* = -5, and the *y*-intercept is *y* = -6.

Draw the graph of the linear equation with an *x*-intercept of 5 and a *y*-intercept of 5.

Draw the graph of the linear equation with an *x*-intercept of -2 and a *y*-intercept of -3.

Answer

Draw the graph of the linear equation with an *x*-intercept of 4 and no *y*-intercept.

Answer