1. Copyright 2013, 2010, 2007, 2005, Pearson, Education, Inc.

2. 3.3
Intercepts

3. Identifying Intercepts
The graph of y = 4x – 8 is shown below. Notice that this graph crosses the y-axis at the point (0, –8). This point is called the y-intercept. Likewise the graph crosses the x-axis at (2, 0). This point is called the x-intercept.
The intercepts are (2, 0) and (0, –8).

4. Helpful Hint
If a graph crosses the x-axis at (2, 0) and the y-axis at (0, –8), then
(2, 0) (0, –8)
Notice that for the x-intercept, the y-value is 0 and for the y-intercept, the x-value is 0.
Note: Sometimes in mathematics, you may see just the number –8 stated as the y-intercept and 2 stated as the x-intercept.
x-intercept
y-intercept

5. Example Identify the x- and y-intercepts. a. b.
x-intercept: (-1, 0), (3, 0)
y-intercept: (0, -3)
x-intercept: (2, 0)

6. Intercepts Finding x- and y-Intercepts
To find the x-intercept, let y = 0 and solve for x.
To find the y-intercept, let x = 0 and solve for y.

7. Example Graph 4 = x – 3y by finding and plotting its intercepts.
To find the y-intercept, let x = 0.
4 = x – 3y
4 = 0 – 3y Replace x with 0.
4 = – 3y Simplify.
= y Divide both sides by –3.
Continued

8. Example (cont) To find the x-intercept, let y = 0. 4 = x – 3y
4 = x – 3(0) Replace y with 0.
4 = x Simplify.
So the x-intercept is (4,0).
Continued

9. Example (cont)
Along with the intercepts, for the third solution, let y = 1.
4 = x – 3y
4 = x – 3(1) Replace y with 1.
4 = x – Simplify.
4 + 3 = x Add 3 to both sides.
7 = x Simplify.
So the third solution is (7, 1).
Continued

10. Graph by Plotting Interceptsx y
Now we plot the two intercepts and (4, 0) along with the third solution (7, 1).
(4, 0)
(7, 1)
(0, )
The graph of 4 = x – 3y is the line drawn through these points.

11. Example Graph 2x = y by finding and plotting its intercepts.
To find the y-intercept, let x = 0.
2(0) = y
0 = y, so the y-intercept is (0,0).
To find the x-intercept, let y = 0.
2x = 0
x = 0, so the x-intercept is (0,0).
It’s the same point. What do we do?
Continued

12. Helpful Hint
Notice that any time (0, 0) is a point of a graph, then it is an x-intercept and a y-intercept. Why? It is the only point that lies on both axes.

13. Example (cont)
Since we need at least 2 points to graph a line, we will have to find at least one more point.
Let x = 3.
2(3) = y
6 = y, so another point is (3, 6).
Let y = 4.
2x = 4
x = 2, so another point is (2, 4).
Continued

14. Example (cont) x y
(3, 6)
(0, 0)
(2, 4)
Now we plot the three solutions (0, 0), (3, 6) and (2, 4).
The graph of 2x = y is the line drawn through these points.

15. Example Graph: x = – 3 This equation can be written x = 0·y – 3.
Any value we substitute for y gives an x-coordinate of –3.
The graph is a vertical line with x-intercept –3, and no y-intercept.
Continued

16. Example (cont) x y
(-3, 0)
The graph of x = –3.

17. Example Graph: y = 3 The equation can be written as y = 0·x + 3.
For any x-value chosen, y is 3.
The graph is a horizontal line with y-intercept 3, and no x-intercept .
Continued

18. Example (cont) x y
(0, 3)
The graph of y = 3.

19. Vertical and Horizontal Linesx y
Vertical lines
The graph of x = c, where c is a real number, is a vertical line with x-intercept (c, 0).
Horizontal lines
The graph of y = c, where c is a real number, is a horizontal line with y-intercept (0, c). x y