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### Course: 8th grade (Illustrative Mathematics)>Unit 3

Lesson 11: Extra practice: 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?

• 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)
• 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
• 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.
• help me... this is so hard.
• 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.
• this doesnt make sense at all I hate this bro
• First, this is the review. Maybe you need to start at the beginning of the lesson to get a better understanding. Ask questions as you go. Do the practice problems to reinforce what you are learning. If you get something wrong, use the hints to find and understand your mistake so you learn how to avoid the error. Then, try the review lesson again.

Here's a quick overview:

The X-intercept is the point where the line crosses the x-axis. So, it must be a point on the x-axis. Any point that is on the x-axis will have a y-value of 0. So, you find the x-intercept by using y=0 in the equation and solve for X. You will then have a point (x-value, 0) that is the x-intercept.

Similarly, the Y-intercept is the point where the line crosses the y-axis, so it must be a point that is on the y-axis. All points on the y-axis have an x-value of 0. Thus, to find the y-intercept, you use x=0 in the equation and solve for Y. You will then have a point (0, y-value) that is the y-intercept.

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.
• is there any way to figure out the x and y intercept from the table? the table thing is really confusing so i wonder if there is any equations for the table itself.
• There are separate formulas for calculating intercepts:

y intercept: if the equation is y=mx+b, the y intercept is b
x intercept: if the equation is y=mx+b, the x intercept is -b/m

To figure out the x and y intercepts from a table, you can use the formula

slope =(y₂ - y₁)/(x₂ - x₁)
and figure out the equation first. Then you plug in the numbers from the table into the equation and use the formulas for the x and y intercepts to figure out what you need.