1. 3
Chapter
Chapter 2
Graphing

2. Section
3.3
Intercepts

3. Identifying Intercepts
Objective 1
Identifying Intercepts

4. Identifying Intercepts
The graph of y = 4x – 8 is shown. 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).

5. 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

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

7. Using Intercepts to Graph a Linear Equation
Objective 2
Using Intercepts to Graph a Linear Equation

8. 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.

9. 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

10. 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

11. 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

12. Example (cont) Now we plot the two intercepts andy
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.

13. 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

14. 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.

15. 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

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

17. Graphing Vertical and Horizontal Lines
Objective 3
Graphing Vertical and Horizontal Lines

18. 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

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

20. 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

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

22. 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