# Intercepts of lines review (x-intercepts and y-intercepts)

CCSS Math: 8.F.A.1, HSF.IF.C.7, HSF.IF.C.7a

The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations.

## What are intercepts?

The $x$-intercept is the point where a line crosses the $x$-axis, and the $y$-intercept is the point where a line crosses the $y$-axis.

*Want a deeper introduction to intercepts? Check out this video.*

## Example: Intercepts from a graph

Looking at the graph, we can find the intercepts.

The line crosses the axes at two points:

The point on the $x$-axis is $(5,0)$. We call this the $x$-intercept.

The point on the $y$-axis is $(0,4)$. We call this the $y$-intercept.

*Want to learn more about finding intercepts from graphs? Check out this video.*

## Example: Intercepts from a table

We're given a table of values and told that the relationship between $x$ and $y$ is linear.

$x$ | $y$ |
---|---|

$1$ | $-9$ |

$3$ | $-6$ |

$5$ | $-3$ |

Then we're asked to find the intercepts of the corresponding graph.

The key is realizing that the $x$-intercept is the point where $y=0$, and the $y$-intercept is where $x=0$.

The point $(7,0)$ is our $x$-intercept because when $y=0$, we're on the $x$-axis.

To find the $y$-intercept, we need to "zoom in" on the table to find where $x=0$.

The point $(0,-10.5)$ is our $y$-intercept.

*Want to learn more about finding intercepts from tables? Check out this video.*

## Example: Intercepts from an equation

We're asked to determine the intercepts of the graph described by the following linear equation:

To find the $y$-intercept, let's substitute $\blue x=\blue 0$ into the equation and solve for $y$:

So the $y$-intercept is $\left(0,\dfrac{5}{2}\right)$.

To find the $x$-intercept, let's substitute $\pink y=\pink 0$ into the equation and solve for $x$:

So the $x$-intercept is $\left(\dfrac{5}{3},0\right)$.

*Want to learn more about finding intercepts from equations? Check out this video.*

## Practice

*Want more practice? Check out these exercises:*