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4.3
Graphing Using Intercepts
1. Given an equation, find the coordinates of the
x- and y-intercepts.
2. Graph linear equations using intercepts.
Standard Form of a Linear Equation in 2-Variables
Ax  By  C
A, B and C are integers.
A≥0
3x  5y  12
No fractions!
A can’t be negative.
Is the given equation written in standard form? If not, rewrite it.
2
x y 2
3
 4x  3 y  7
No, can’t have fractions.
No, A can’t be negative.
2x + 3y = 6
4x - 3y = -7
2 y  5x  3
x  2 y  4
No, x term must be written first.
5x – 2y = -3
A: Yes
B: No
Yes.
Objective 1
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Given an equation, find
the coordinates of the
x- and y-intercepts.
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)
The point where a graph
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?
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.
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!
Example 2
Find the x- and y-intercepts for 3x  2 y  18
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)
Example 3
Find the x- and y-intercepts for y  3x  4
x-intercept: let y = 0
0  3x  4
 4  3x
4
x
3
 4 
  ,0 
 3 
y-intercept: let x = 0
y  30   4
y4
0 , 4 
Example 4
Find the x- and y-intercepts for
x-intercept: let y = 0
0=6
Not true.
Horizontal line.
No x-intercept.
y6
y-intercept: let x = 0
0x + y = 6
y=6
(0, 6)
Example 5
Find the x- and y-intercepts for x  4
x-intercept: let y = 0
y-intercept: let x = 0
x + 0y = -4
0 = -4
x = -4
Not true.
Vertical line.
No y-intercept.
(-4, 0)
Objective 2
Graph linear equations using
intercepts.
Example 6
Graph: 7x – 2y = 14
From Example 1:
x-intercept: (2, 0)
y-intercept: (0, -7)
7x – 2y = 14
Example 7
Graph: y  2 x  8
x-intercept:
(-4, 0)
y-intercept:
(0, 8)
Example 8
Graph: 4 x  5 y  0
x-intercept:
(0, 0)
y-intercept:
(0, 0)
Need another point.
Choose a value for x or y and solve.
(5, -4)
Example 9
Graph:
y  3
Equation has only a y.
Line intersects only the y-axis.
Horizontal line through -3.
What is the x-intercept for 3x – y = 6?
a) (2, 0)
b) (0, –6)
c) (–6, 0)
d) (0, 2)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 4- 17
What is the x-intercept for 3x – y = 6?
a) (2, 0)
b) (0, –6)
c) (–6, 0)
d) (0, 2)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 4- 18
What is the y-intercept for y = 2x – 6?
a) (3, 0)
b) (0, –6)
c) (–6, 0)
d) (0, 3)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 4- 19
What is the y-intercept for y = 2x – 6?
a) (3, 0)
b) (0, –6)
c) (–6, 0)
d) (0, 3)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 4- 20