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

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.

## 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.

## Example: Intercepts from an equation

We're asked to determine the intercepts of the graph described by the following linear equation:
$3x+2y=5$
To find the $y$-intercept, let's substitute $\blue x=\blue 0$ into the equation and solve for $y$:
\begin{aligned}3\cdot\blue{0}+2y&=5\\ 2y&=5\\ y&=\dfrac{5}{2}\end{aligned}
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 $x$:
\begin{aligned}3x+2\cdot\pink{0}&=5\\ 3x&=5\\ x&=\dfrac{5}{3}\end{aligned}
So the $x$-intercept is $\left(\dfrac{5}{3},0\right)$.