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

Lesson 2: 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.
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 $\left(7,0\right)$ 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.
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:
$3x+2y=5$
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 $\left(\frac{5}{3},0\right)$.
Want to learn more about finding intercepts from equations? Check out this video.

## 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 was sort of an obligation for me to be here but by seeing the progress I made in only 9 days ( i used to know almost nothing about math) I'm now addicted to learning it and i can't stop it's really fun
(my eyes are burning from the screen rn cuz i've been studying for hours straight)
• 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.
• if the question is y=5x+random number how to find x intercept?
• In all equations, you find the x-intercept by using y=0 in the equation and solving for x.
• how do i put a fraction in
• this type of stuff is soooo confusing and too me it give off little explaination when it be like "well we r gon' to zoom in" like child what in da world how do we "zoom in" or "zoom out"? i am i 8th grade but sometime when oing this math it makes me feel like a 9th grader in the 8th grade!! does anyone else agree?
• i mean, teachers do say 8th grade is just a transition to 9th, or maybe thats just my school, who knows.
• 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]