1. Intercepts

2. Objectives To learn what intercepts are
To learn how to find x and y-intercepts of a graph
To learn how to find x and y-intercepts of an equation
To use x and y-intercepts to sketch a graph

3. What are intercepts?
An intercept is where something intersects or touches
For example,
an x-intercept is where it touches the x-axis
a y-intercept is where it touches the y-axis

4. Intercepts of a Graph (5, 0) (0, 7)y
What are the x-intercept and y-intercept of the graph at right?
X-intercept:
Y-intercept:
(0, 7) x
(5, 0)
(5, 0)
(0, 7)
Where it touches the y-axis
Where it touches the x-axis

5. Intercepts of a Graph (-8, 0) (0, 6)y
What are the x-intercept and y-intercept of the graph at right?
X-intercept:
Y-intercept:
(0, 6) x
(-8, 0)
(-8, 0)
(0, 6)
Where it touches the y-axis
Where it touches the x-axis

6. Intercepts of a Graph (-9, 0) (3, 0) (0, -5) (0, -8)
What are the x and y-intercepts of the graphs below?
Notice:
For all the
x-intercepts the
y-coordinate is ____
y-intercepts the
x-coordinate is ____
(-9, 0)
X-intercept:
(3, 0)
X-intercept:
(0, -5)
Y-intercept:
(0, -8)
Y-intercept:

7. Which are which? T, V, W, X S, U, W, Y
Which of the coordinates below are x-intercepts?
Which of the coordinates below are y-intercepts?
T, V, W, X
S, U, W, Y
R(3, 5) S(0, 9) T(-2, 0) U(0, 1) V(15, 0)
W(0, 0) X( ½ , 0) Y(0, 8) Z(1, 0.5)

8. Intercepts of an Equation
We know for an x-intercept the ______________ is 0
In the y-intercept the ___________ is 0
We can use this to solve equations.
To solve for an x-intercept plug in a 0 for y.
To solve for a y-intercept plug in a 0 for x.
Y-coordinate
x-coordinate

9. Intercepts of an Equation
Find the x and y-intercepts of the equation -2x + 3y = 19
To find the y-intercept plug in 0 for _____
To find the x-intercept plug in 0 for _____ x y
-2x + 3y = 19
-2x + 3y = 19
-2(0) + 3y = 19
-2x + 3(0) = 19
0 + 3y = 19
-2x + 0 = 19
3y = 19
-2x = 19
y = 6.3
( 0, 6.3)
x = -9.5
( -9.5, 0)

10. Intercepts of an Equation
Find the x and y-intercepts of the equation y
To find the x-intercept plug in 0 for _____
To find the y-intercept plug in 0 for _____ x
5* *5
-80=-4x
x = 20
(20, 0)
y = 16
(0, 16)

11. Sketching a Graph from Intercepts
Find the intercept of the equation 3x + y = and sketch the graph
X-intercept: (Plug in 0 for y)
3x + 0 = 12
3x = 12
x = 4
(4, 0)
Y-intercept: (Plug in 0 for x)
3(0) + y = 12
0 + y = 12
y = 12
(0, 12)

12. Sketching a Graph from Intercepts
Find the intercept of the equation
and sketch the graph
X-intercept: (Plug in 0 for y)
2* *2
x = 6
(6, 0)
Y-intercept: (Plug in 0 for x)
y = 0 – 3
y = -3
(0, -3)

13. Conclusion Intercept is : _____________________
The x-intercept is _________________
The y-intercept is _________________
To find the x-intercept of an equation ____________________
To find the y-intercept of an equation ____________________
Where something intersects or touches
Where it touches the x-axis
Where it touches the y-axis
Plug in 0 for Y
Plug in 0 for X