X and Y Intercepts

Finding X and Y Intercepts
Using Graphs and Equations

In this lesson, you will learn:
What x and y intercepts are.
How to find x and y intercepts on a graph.
How to find x and y intercepts using an equation.
How to graph a line using its intercepts.

x- and y-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.

​There are two ways to write intercepts.
You can write the coordinates of the intercept as shown in this graph:
the x-intercept is (-4, 0) and
the y-intercept is (0, 6)
OR
You can just write:
the x-intercept is -4 and,
the y-intercept is 6

Finding X- and Y- Intercepts from a Graph

• The x-intercept is the point where a line crosses the x-axis.

• The y-intercept in the point where a line crosses the y-axis.

Multiple Choice

What's the definition of x-intercept?

• Where the graph crosses the x axis
• where the graph crosses the y axis

Multiple Choice

Identify the x-intercept of this graph.

• (-2, 0)

• (-3, 0)

• (0, 3)

• (2, 0)

Multiple Choice

What is the y-intercept of this graph.

• (0, -4)

• (-4, 0)

• (0, -2)

• (-2, 0)

Multiple Choice

What are the x- and y-intercepts, respectively, on this graph?

• (0, 5), (0, 5)

• (5, 0), (5, 0)

• (5, 0), (0, 5)

• (0, 0), (5, 0)

Multiple Choice

Identify the x- and y-intercepts of the line graphed in the picture.

• x-intercept: Undefined

  y-intercept: 0

• x-intercept: (0,-2.8)

  y-intercept: (-3.5,0)

• x-intercept: (-3.5,0)

  y-intercept: (0,-2.8)

• x-intercept: (3.5,0)

  y-intercept: (0,2.8)

Multiple Choice

Identify the x- and y-intercepts of this graph.

• They are both (0,0).

• They cannot be determined from the graph.

• x-intercept is (0,0).

  y-intercept is (0,-1)

• None of the above

Multiple Choice

Identify the x-intercept of this graph.

• None

• (4,0)

• (0,4)

• Undefined

Multiple Choice

Does this graph have an x-intercept?

• Yes

• No

• It is not possible to determine from the graph.

Using an Equation to Find Intercepts

If you don't have a graph, you can still find the x- and y-intercepts of a linear function by using the equation of the function.


The next slide shows how to find the intercepts for a linear function with the equation 3x + 4y = 24.

Finding Intercepts Algebraically

Here is another example of finding the intercepts of a linear function using its equation.
Plug in zero for the other coordinate.

Multiple Choice

Give the x-intercept of
3x + 8y = 24

• (8, 0)
• (0, 8)
• (3, 0)
• (0, 3)

Multiple Choice

Give the y-interecept of
3x + y = 5

• (-3, 0)
• (0,5)
• (5, 0)
• (0, -3)

Multiple Choice

Find the x-intercept of the equation:

$$y=2x-4$$  

• (-4,0)

• (2,0)

• (0,2)

• (0,-4)

Multiple Choice

Identify the y-intercept of the equation:

$$y=3x-9$$  

• (0,3)
  

• (0,-9)

• (9,0)

• (3,0)

Multiple Choice

What is the x- and y-intercept for the following equation ?
4x - 10y = 20

• x - int = 4    
  y-int = -10
• x-int = 5
  y-int = 2
• x - int = 5
  y int = -2
• x -int = 4
  y -int = -10

Multiple Choice

Name the x- and y-intercepts for the equation:
2x + y = 6

• (0, 3) and (6, 0)

• (0, -3) and (-6, 0)

• (3, 0) and (0, 6)

• (-3, 0) and (0, -6)

Multiple Choice

Identify the y-intercept of the equation:

$$y=x$$  

• (0,0)

• (1,0)

• The is no y-intercept

Multiple Choice

At the x-intercept, the value of y is _______.

• 1

• 0

• x

• y

Multiple Choice

At the y-intercept, the value of x is _______________

• x

• y

• 1

• 0

​Graphing Using Intercepts

Now that you can find the intercepts using an equation, you can graph the linear function by graphing the two intercepts and connecting them with a line.

The next slide gives the steps and an example of how to do this.

Graphing Using Intercepts

1. Find the x-intercept by setting y = 0 and solving for x.

2. Graph the x-intercept

3. Find the y-intercept by setting x = 0 and solving for y.

4. Graph the y-intercept

5. Draw a line connecting the 2 points

Graphing

Graph the linear function with the equation 4x - 3y = 24 using its x- and y-intercepts.

Graphing

Graph the linear function with the equation y = -3x + 6 using its x- and y-intercepts.