1. Graphing Using Intercepts
4.3
Graphing Using Intercepts
1. Given an equation, find the coordinates of the x- and y-intercepts.
2. Graph linear equations using intercepts.

2. Standard Form of a Linear Equation in 2-Variables
A, B and C are integers.
A ≥ 0
No fractions!
A can’t be negative.

3. Is the given equation written in standard form? If not, rewrite it.
No, A can’t be negative.
4x - 3y = -7
No, can’t have fractions.
2x + 3y = 6
Yes.
No, x term must be written first.
5x – 2y = -3
A: Yes
B: No

4. Given an equation, find the coordinates of the x- and y-intercepts.
Objective 1
Given an equation, find the coordinates of the x- and y-intercepts.
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5. The point where the graph crosses an axis is called an intercept.
The point where a graph
intersects the x-axis is called
the x-intercept.
(4, 0)
intersects the y-axis is called
the y-intercept.
(0, -2)
x-intercept (4, 0)
y-intercept (0, 2)
What do you notice about the intercepts?

6. To find an x-intercept:
To find a y-intercept:
1. Let y = 0.
1. Let x = 0.
2. Solve for x.
2. Solve for y.

7. Find the x- and y-intercepts for 7x – 2y = 14
Example 1
Find the x- and y-intercepts for 7x – 2y = 14
x-intercept: let y = 0
7x – 2y = 14
7x – 2(0) = 14
7x = 14
x = 2
x-intercept: (2, 0)
y-intercept: let x = 0
7x – 2y = 14
7(0) – 2y = 14
–2y = 14
y = –7
y-intercept: (0, –7)
Always write an ordered pair!

8. Find the x- and y-intercepts for
Example 2
Find the x- and y-intercepts for
x-intercept: let y = 0
3x + 2(0) =18
3x = 18
x = 6
x-intercept: (6, 0)
y-intercept: let x = 0
3(0) + 2y = 18
2y = 18
y = 9
y-intercept: (0, 9)

9. Find the x- and y-intercepts for
Example 3
Find the x- and y-intercepts for
x-intercept: let y = 0
y-intercept: let x = 0

10. Find the x- and y-intercepts for
Example 4
Find the x- and y-intercepts for
x-intercept: let y = 0
y-intercept: let x = 0
0 = 6
Not true.
Horizontal line.
No x-intercept.
0x + y = 6
y = 6
(0, 6)

11. Find the x- and y-intercepts for
Example 5
Find the x- and y-intercepts for
x-intercept: let y = 0
y-intercept: let x = 0
x + 0y = -4
x = -4
(-4, 0)
0 = -4
Not true.
Vertical line.
No y-intercept.

12. Objective 2
Graph linear equations using intercepts.

13. Graph: 7x – 2y = 14 From Example 1: x-intercept: (2, 0)
y-intercept: (0, -7)
7x – 2y = 14

14. Example 7
Graph:
x-intercept:
(-4, 0)
y-intercept:
(0, 8)

15. Graph: x-intercept: y-intercept: Need another point.
Example 8
Graph:
x-intercept:
(0, 0)
y-intercept:
Need another point.
Choose a value for x or y and solve.
(5, -4)

16. Graph: Example 9 Equation has only a y.
Line intersects only the y-axis.
Horizontal line through -3.

17. What is the x-intercept for 3x – y = 6?
b) (0, –6)
c) (–6, 0)
d) (0, 2)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

18. What is the x-intercept for 3x – y = 6?
b) (0, –6)
c) (–6, 0)
d) (0, 2)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

19. What is the y-intercept for y = 2x – 6?
b) (0, –6)
c) (–6, 0)
d) (0, 3)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

20. What is the y-intercept for y = 2x – 6?
b) (0, –6)
c) (–6, 0)
d) (0, 3)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley