Main content

## 8th grade (Illustrative Mathematics)

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

Lesson 11: Extra practice: Intercepts# Intercepts of lines review (x-intercepts and y-intercepts)

CCSS.Math: , ,

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 parenthesis, 5, comma, 0, right parenthesis. We call this the x-intercept.

The point on the y-axis is left parenthesis, 0, comma, 4, right parenthesis. 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 | minus, 9 |

3 | minus, 6 |

5 | minus, 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, equals, 0, and the y-intercept is where x, equals, 0.

The point left parenthesis, 7, comma, 0, right parenthesis is our x-intercept because when y, equals, 0, we're on the x-axis.

To find the y-intercept, we need to "zoom in" on the table to find where x, equals, 0.

The point left parenthesis, 0, comma, minus, 10, point, 5, right parenthesis 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 start color #6495ed, x, end color #6495ed, equals, start color #6495ed, 0, end color #6495ed into the equation and solve for y:

So the y-intercept is left parenthesis, 0, comma, start fraction, 5, divided by, 2, end fraction, right parenthesis.

To find the x-intercept, let's substitute start color #ff00af, y, end color #ff00af, equals, start color #ff00af, 0, end color #ff00af into the equation and solve for x:

So the x-intercept is left parenthesis, start fraction, 5, divided by, 3, end fraction, comma, 0, right parenthesis.

*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(71 votes)
- I agree. I'm in eighth and confused.(30 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(4 votes)

- How do i find the y and x intercepts of an equation in standard form??(11 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.(10 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 put a fraction in(8 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)

- 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)

- x - (y + 11) = 3(x - 2y -1)

Help me solve this plss(5 votes)- (assuming you want to find the intercepts)

X-intercept (plug in 0 for y)

x - (y + 11) = 3(x - 2y - 1)

x - (0 + 11) = 3(x - 2(0) - 1)

x - 11 = 3x - 3

x = 3x + 8

4x = 8

x = 2

Y-intercept (plug in 0 for x)

x - (y + 11) = 3(x - 2y - 1)

0 - (y + 11) = 3(0 - 2y - 1)

-y - 11 = -6y - 3

-y = -6y + 8

5y = 8

y = 8/5 or 1.6(0 votes)