1. MTH 070 Elementary Algebra I
Chapter 3
Linear Equations, Slope, Inequalities,
and Introduction to Functions
Section 3.2
The Intercept Method
Copyright © 2010 by Ron Wallace, all rights reserved.

2. ? Linear Equations Ax + By = C y = mx + b
Any equation equivalent in form to …
Ax + By = C
A, B, & C are constants
Standard Form (this section)
A second common form …
y = mx + b
m & b are constants
Slope-Intercept From (next section) ?

3. The amount of gas in your tank as you drive.
(0,16)
What is significant about these two points?
Intercepts!
(320,0)

4. What is true about every point on the x-axis?
The y value in the ordered pair is 0.
(0,0)
(-3,0)
(1,0)

5. What is true about every point on the y-axis?
The x value in the ordered pair is 0.
(0,2)
(0,0)
(0,-1)

6. Intercepts x-intercept: Point where the line crosses the x-axis.
(3, 0)
y-intercept:
Point where the line crosses the y-axis.
(0, 2)

7. Will every line cross both axes?
Intercepts
x-intercept:
Point where the line crosses the x-axis.
(3, 0)
y-intercept:
Point where the line crosses the y-axis.
(0, 2)
Will every line cross both axes?

8. Given and Equation Find the Intercepts
2x – 5y = 12
x-intercept:
Let y = 0
Solve for x
2x – 5(0) = 12
2x = 12
x = 6
x-intercept: (6, 0)
y-intercept:
Let x = 0
Solve for y
2(0) – 5y = 12
–5y = 12
y = –12/5
y-intercept: (0, –12/5)

9. Standard Form Find the Intercepts – Pattern?
Ax + By = C
x-intercept:
Let y = 0
Solve for x
Example
7x + 2y = 8
y-intercept:
Let x = 0
Solve for y

10. Using Intercepts to Graph a Line
2x – 5y = 12
x-intercept:
(6, 0)
y-intercept:
(0, -12/5) 1
Check?

11. Lines that Pass Through the Origin
x-intercept?
(0,0)
y-intercept?
What will be true about the equation?
Ax + By = C
Graphing will require a second point.
Lines through the origin:
Ax + By = 0
y = mx

12. Horizontal Lines Horizontal Lines: y = b x-intercept? DNE y-intercept?
(0, 2)
What will be true about every point on this line?
y = 2 … (x, 2)
What will be true about the equation?
Ax + By = C
Horizontal
Lines:
y = b

13. Vertical Lines Vertical Lines: x = a x-intercept? (1, 0) y-intercept?
DNE
What will be true about every point on this line?
x = 1 … (1, y)
What will be true about the equation?
Ax + By = C
Vertical
Lines:
x = a

14. y = 0 x = 0 One more thing … What is the equation of the x-axis?
What is the equation of the y-axis?
x = 0