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## Algebra 1

### Course: Algebra 1>Unit 4

Lesson 4: x-intercepts and y-intercepts

# 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 $\left(5,0\right)$. We call this the $x$-intercept.
The point on the $y$-axis is $\left(0,4\right)$. 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 $\left(7,0\right)$ 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 $\left(0,-10.5\right)$ 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 $x=0$ into the equation and solve for $y$:
$\begin{array}{rl}3\cdot 0+2y& =5\\ 2y& =5\\ y& =\frac{5}{2}\end{array}$
So the $y$-intercept is $\left(0,\frac{5}{2}\right)$.
To find the $x$-intercept, let's substitute $y=0$ into the equation and solve for $x$:
$\begin{array}{rl}3x+2\cdot 0& =5\\ 3x& =5\\ x& =\frac{5}{3}\end{array}$
So the $x$-intercept is $\left(\frac{5}{3},0\right)$.

## Practice

Problem 1
Determine the intercepts of the line graphed below.
$x$-intercept:
$\left($
$,$
$\right)$
$y$-intercept:
$\left($
$,$
$\right)$

Want more practice? Check out these exercises:

## Want to join the conversation?

• im in 8th and its hard to keep all this stuff in your head
• I agree. I'm in eighth and confused.
• help me solve this problem step by step 1/3x-2 find the x,y intercept
• there is no interception points because that isn't a linear equation
• Math can be fun sometimes if you do it right lol
• it's fun if your good at it
or if you just like it
I like linear equations the best, what about u peeps
• How do i find the y and x intercepts of an equation in standard form??
• You can always find the X-intercept by setting Y to 0 in the equation and solve for X.

Similarly, you can always find the Y-intercept by setting X to 0 in the equation and solve for Y.

Hope this helps.
• how do i put a fraction in
• what is the x- intercept in the equation y=8/-1x-22
• To find x-intercept, take y=0
0 = 8/-1x-22
-x-22 = 8
-x = -8 + 22
-x = 14
x = -14
Therefore, x-intercept = (-14,0) [Assuming I got your question right]
• How do i know what do add by ? i keep adding by the half of what we adding or subtracting and i still down get the answers correct .
• One way you could do it is to visualize the values on a line that has negative and positive graduations, then count how many times you're moving 1 graduation at a time.
For example: to go from -6 to -4, you need to move:
- from -6 to -5 (in the positive direction),
- then from -5 to -4 (in the positive direction),
So in total you moved 2 times in the positive direction so: +2
Hope this helps?