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## Algebra 1

### Unit 4: Lesson 4

x-intercepts and y-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?

- help me solve this problem step by step 1/3x-2 find the x,y intercept(22 votes)
- there is no interception points because that isn't a linear equation(3 votes)

- im in 8th and its hard to keep all this stuff in your head(3 votes)
- I agree. I'm in eighth and confused.(21 votes)

- How do i find the y and x intercepts of an equation in standard form??(10 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.(4 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](10 votes)

- how do i put a fraction in(7 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 .(4 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?(6 votes)

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

Help me solve this plss(6 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)

- I don't understand anything F(4 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,#).(4 votes)

- When my students use an iPad, it is writing -3/4 as -3 divided by 4 and counts the answer wrong. When they tried to re-enter it as -0.75, it still counted it wrong. Is that because the program counted that question as "wrong" already, and the "rewrite" does not change the fact it was "wrong" first?(3 votes)
- The same thing happened with me but they want the answer in fraction form, not decimal.(1 vote)

- why don't we use the slope of line to find intercept?(1 vote)
- You can use the slope if you are graphing but sometimes that is more work because you would have to graph out the points and the slope then find the intercepts.(3 votes)