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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 $(5,0)$ . 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:*

## Want to join the conversation?

- im in 8th and its hard to keep all this stuff in your head(88 votes)
- I agree. I'm in eighth and confused.(42 votes)

- help me solve this problem step by step 1/3x-2 find the x,y intercept(26 votes)
- there is no interception points because that isn't a linear equation(5 votes)

- Math can be fun sometimes if you do it right lol(18 votes)
- it's fun if your good at it

or if you just like it

I like linear equations the best, what about u peeps(7 votes)

- How do i find the y and x intercepts of an equation in standard form??(13 votes)
- 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.(12 votes)

- how do i put a fraction in(9 votes)
- what is the x- intercept in the equation y=8/-1x-22(5 votes)
- 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](11 votes)

- 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 .(5 votes)
- 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?(9 votes)

- if the question is y=5x+random number how to find x intercept?(4 votes)
- In all equations, you find the x-intercept by using y=0 in the equation and solving for x.(9 votes)

- I don't understand anything F(5 votes)
- That is hard to believe. Do you know the difference between the x and y axis? Do you understand what intercept means? Then just learn that the x intercept is where y = 0 (on the x axis) and the y intercept is where x = 0 (on the y axis). You always need a 0 for an intercept, x int is (#,0) and y int is (0,#).(5 votes)

- 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?(4 votes)
- i mean, teachers do say 8th grade is just a transition to 9th, or maybe thats just my school, who knows.(4 votes)