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Math 60
Chapter 6.5A
Supplement Finding the X and Y Intercepts
And Graphing the Line (10/89)
The y-Intercept
Suppose you are given an equation
say for instance:
2 x  y  3 and you are asked to graph it. Pick out 5 ordered pairs that satisfy this equation,
x
y
-1
5
0
3
1
1
2
-1
3
-3
Its graph would look like this:
Notice where this line crosses the y-axis. It crosses it at the point (0,3). We call this the y-intercept.
Definition: The y-intercept is the point where a line crosses the y-axis.
Notice in the previous example that at the y-intercept we have an x-coordinate of zero because these points are on the y-axis.
Any point on the y-axis has a first coordinate of zero.
Keeping this in mind, it is easy to determine the y-intercept of any equation simply by letting x be zero. Then solving for y, you
can determine the y-intercept.
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MATH 60
UNIT 6.5A
2
Example 1: Find the y-intercept in each of the given equations.
(a) Given: 5x + y = -2
To find the y intercept, let x = 0

5 * 0 + y = -2

Solve for y.
0 + y = -2
y = -2
Therefore, the y-intercept is at (0,-2).
(b) Given: 3x – y = 1
Let x = 0 and solve for y.

3*0  y  1
0 y 1
y  1
Therefore, the y-intercept is at (0,-1).
(c) Given: 2 x  5 y  10
Let x = 0 and solve for y.
2*0  5 y  10
0  5 y  10
5 y  10

1
1
* 5 y  * 10
5
5
y2
Therefore, the y-intercept is at (0,2).
Exercise 1: Find the y intercept for each of the following equations.
1.x  y  17
(____, ____)
3.x  y  2
(____, ____)
5.5 x  4 y  24
(____, ____)
2. 6 x  y  6
(____, ____)
4. 2 x  3 y  0
(____, ____)
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MATH 60
UNIT 6.5A
3
The x-intercept
Definition: The x-intercept is the point where a line crosses the x-axis.
Any point on the x-axis has a second coordinate of zero. So it would be easy to determine the x-intercept of any equation simply
by letting y = 0 and solving for x.
Example 2: Find the x-intercept in each of the given equations.
(a) Given: x + y = -7
Let y = 0 and solve for x.
x  0  7
x  7

Therefore, the x-intercept is at (-7,0).
(b) Given: y = -x + 2
Let y = 0 and solve for x.
0  x  2

0  x  x  x  2
x2
Therefore, the x-intercept is at (2,0).
(c) Given: 2x - 3y = -8
2 x  3*0  8
2 x  8
Let y = 0 and solve for x.

1
1
* 2 x  * 8
2
2
x  4
Therefore, the x-intercept is at (-4,0).
Exercise 2: Find the x- and y-intercept for each of the following equations.
1. 2 x  y  8
(___, ___);(___, ___)
3. 5 x  2 y  10
(___, ___);(___, ___)
2. x  y  18
(___, ___);(___, ___)
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No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.
MATH 60
UNIT 6.5A
4
Example 3: Graph 4x + 8y = 16 by finding the x- and y-intercepts.
(a)
4 x  8*0  16
4 x 16

4
4
x4
Therefore, the x-intercept is (4,0)
(b)
4*0  8 y  16
8 y 16

8
8
y2
Therefore, the y-intercept is (0,2).
Exercise 3: Graph the following lines using x- and y-intercepts (See pages 5 and 6 for answers).
1. y  x  5
2. 3 x  2 y  12
3. 2 x  y  6
4. x  3 y  3
5. 2 x  y  4
6. 5 x  10 y  20
7. 7 y  3 x  21
8. 3 y  2 x  6
9. 6 y  3 x  18
10.  2 x  4 y  12
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MATH 60
UNIT 6.5A
5
Answers
Exercise 1
1. (0,17)
Exercise 2
1. (4,0);(0, 8)
2. (0, 6)
3. (0, 2)
4. (0,0)
2. (18,0);(0, 18)
5. (0, 6)
3. (2,0);(0, 5)
Exercise 3
1.
2.
3.
4.
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MATH 60
UNIT 6.5A
5.
6.
7.
8.
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MATH 60
9.
UNIT 6.5A
10.
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No part of this work may be reproduced without the prior written consent of the Cerritos College Math Learning Center.
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