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### Course: Algebra (all content) > Unit 3

Lesson 2: x-intercepts and y-intercepts- Intro to intercepts
- x-intercept of a line
- Intercepts from a graph
- Intercepts from an equation
- Intercepts from an equation
- Intercepts from a table
- Intercepts from a table
- Graphing using intercepts (old)
- Intercepts of lines review (x-intercepts and y-intercepts)

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# 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.

*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.

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 ${x}={0}$ into the equation and solve for $y$ :

So the $y$ -intercept is $(0,{\displaystyle \frac{5}{2}})$ .

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

So the $x$ -intercept is $({\displaystyle \frac{5}{3}},0)$ .

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

## Practice

*Want more practice? Check out these exercises:*

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