Download H:\Courses at PSTCC\1030 and 00

Graphing Linear Equations Using Intercepts - Section 3.2
An x-intercept of a graph is the x-coordinate of a point where the graph intersects the x-axis. The y-coordinate
corresponding to an x-intercept is always zero. Alternatively, the x-intercept can be listed as an ordered pair x, 0
where x is the x-coordinate of the point where the graph intersects the x-axis.
A y-intercept of a graph is the y-coordinate of a point where the graph intersects the y-axis. The x-coordinate
corresponding to a y-intercept is always zero. Alternatively, the y-intercept can be listed as an ordered pair 0, y
where y is the y-coordinate of the point where the graph intersects the y-axis.
Identify the x- and y-intercepts for each graph below:
-5
-4
-3
-2
5
5
4
4
3
3
2
2
1
1
-1
1
2
3
4
5
-5
-4
-3
-2
-1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
2
3
4
5
All equations of the form Ax By C where A, B, and C are real numbers and A and B are both not zero will
appear as lines when graphed. This form is called the standard form of the equation of a line (or general form of
the equation of a line).
Find the x- and y-intercepts for the graph of each line:
3x
x
5y
4y
15
7
1
Using Intercepts to Graph Ax
By
C
1. Find the x- and y-intercepts.
2. (Optional) Find a third point (check point)
3. Draw line passing through these points.
Graph 2x
3y
6
5
4
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5
-1
-2
-3
-4
-5
2
Graph x
2y
1
5
4
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5
1
2
3
4
5
-1
-2
-3
-4
-5
Graph 3x
y
0
5
4
3
2
1
-5
-4
-3
-2
-1
-1
-2
-3
-4
-5
3
Equations of Horizontal and Vertical Lines
Remember the graph of the equation Ax By
them could be zero. What happens in this case?
C is a line provided A and B are NOT both zero. However, one of
Use a table of values to graph the following linear equations:
Graph y
1
x
y
1
x, y
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5
1
2
3
4
5
-1
-2
-3
Graph x
4
x
4
y
x, y
3
2
1
-5
-4
-3
-2
-1
-1
-2
-3
The graph of the equation y
b is a horizontal line with a y-intercept of 0, b .
The graph of the equation x
a is a vertical line with a x-intercept of a, 0 .
4
Application
A new car sold for $24,000, but depreciates in value by $3000 per year. Write a linear equation in two variables
that models the car’s value, y, in dollars x years after it is purchased.
Find the x-intercept for your equation and describe in words what this means in terms of the car’s value.
Find the y-intercept for your equation and describe in words what this means in terms of the car’s value.
Graph your equation below and use it to estimate the car’s value after 5 years. Label and scale each axis
appropriately. Compare this estimate to the value obtained using your equation.
25000
20000
15000
10000
5000
0
0
1
2
3
4
5
6
7
8
9
10
5