Download CHAPTER 7: Graphing Linear Equations

MATH 0960
7.1 Notes
CHAPTER 7: Graphing Linear Equations
Section 7.1: The Cartesian Coordinate System and Linear Equations in Two Variables
Topics:
A. Plot points in the Cartesian coordinate system.
B. Determine whether an ordered pair is a solution to a linear equation.
C. Solve applications.
A. Plot points in the Cartesian coordinate system.
 What does a problem look like?
Example: Plot the following points on the
same axes. Make sure you label your axes
and points.
1. ( )

2. (
)
3. (
)
What do I need to know?
o The Cartesian coordinate system is
made up of two perpendicular number
lines called the x-axis (horizontal)) and
the y-axis (vertical).
o The point of intersection between the axes is called the origin.
o Points, or ordered pairs, are given by their distance from zero along each
axis in the form: (
)
B. Determine whether an ordered pair is a solution to a linear equation.
 What does a problem look like?
Is ( ) a solution to the equation
?

Answer: No.
What do I need to know?
o If an ordered pair is a solution to a linear equation the x and y values can be
substituted to make a true statement.
o “A graph of an equation in two variables is an illustration of the set of points
whose coordinates satisfy [are solutions of] the equation.” – page 407
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MATH 0960
7.1 Notes
o “A set of points that are on a line are said to be collinear.” – page 407
Example: Determine whether the
three points appear to be collinear.
)
1. ( ) ( ) (
2. (
3. (
)(
(
)
)(
)
)
(
)
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MATH 0960
7.1 Notes
C. Solve applications.
 What does a problem look like?
Example: The graph to the right depicts cost vs. mileage for two rental
companies: U-Move and Bargain. Use the graph to answer questions below.
Rental Cost
45
U-Move
Bargain
40
35
Cost (USD)
30
25
20
15
10
5
0
0
10
20
30
40
50
60
70
Mileage
80
90
100
110
120
1. Find the ordered pair representing the point at which the lines cross. This
represents the mileage and cost for when the two companies charge the
same amount.
Answer: (
)
2. What is the base price of each rental, that is, what is the cost if the mileage is
zero?
Answer: U-Move is $10, Bargain is $20
3. How much does each rental cost if 120 miles are driven?
Answer: U-Move costs $40, Bargain costs $38
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