Download Graphing Linear Equations

GRAPHING LINEAR
EQUATIONS
THE RECTANGULAR COORDINATE SYSTEM
The Academic Support Center @ Daytona State College (Math, Page 1 of 19)
Rectangular Coordinate System
Graphing on a line
0
VS.
Graphing on a coordinate plane
The Academic Support Center @ Daytona State College (Math, Page 2 of 19)
Rectangular Coordinate System
origin
x-axis
y-axis
quadrant
ordered pair
horizontal
vertical
slope
The Academic Support Center @ Daytona State College (Math, Page 3 of 19)
Rectangular Coordinate System
Plot the points
(3, 5)
(-4, 0)
(2, -1)
(-5, -6)
(0, 3)
(4, 4)
The Academic Support Center @ Daytona State College (Math, Page 4 of 19)
Rectangular Coordinate System
Give the coordinates of
the ordered pairs.
The Academic Support Center @ Daytona State College (Math, Page 5 of 19)
Linear Equations in Two Variables
Determine if the ordered pair is a solution to the linear equation.
2x – 3y = 9
x = 2y + 5
(0, -3)
(-6, 1)
7
(1, - 3)
(3, 12)
1
(2 , 6)
5
(0, - 2 )
The Academic Support Center @ Daytona State College (Math, Page 6 of 19)
Interpreting a Graph
A taxi company in Daytona Beach charges
$5.00 for any distance up to the first mile
and $3.00 for every mile thereafter. The
cost of a cab ride can be modeled
graphically.
y
$
1. Why is the first part of the model
represented by a horizontal line?
2. What does the y-intercept mean in
this problem?
3. Why is the rest of the line not
horizontal?
4. How much would it cost to take a cab
7.5 miles?
50
40
30
20
10
2
4
Miles
6
8
x
The Academic Support Center @ Daytona State College (Math, Page 7 of 19)
Graphing Linear Equations
Making a Table of Values
x
y
4x – y = 6
-1
1
2
The Academic Support Center @ Daytona State College (Math, Page 8 of 19)
Graphing Linear Equations
Making a Table of Values
3x + 2y = 6
x
y
The Academic Support Center @ Daytona State College (Math, Page 9 of 19)
Graphing Linear Equations
Making a Table of Values
- 2y = 6
x
y
The Academic Support Center @ Daytona State College (Math, Page 10 of 19)
Graphing Linear Equations
Making a Table of Values
5x = -15
x
y
The Academic Support Center @ Daytona State College (Math, Page 11 of 19)
Graphing Linear Equations
Making a Table of Values
𝟏
𝟐
y= x-3
x
y
The Academic Support Center @ Daytona State College (Math, Page 12 of 19)
Finding the y-intercept
Replace x in the equation
with zero and solve for y
- 2x – y = - 4
The Academic Support Center @ Daytona State College (Math, Page 13 of 19)
Finding the x-intercept
Replace y in the equation
with zero and solve for x
- 2x – y = - 4
The Academic Support Center @ Daytona State College (Math, Page 14 of 19)
Graphing using x and y
intercepts
x – intercept (
y – intercept (
) on the x axis
) on the y axis
The Academic Support Center @ Daytona State College (Math, Page 15 of 19)
Graph using intercepts
3y = -5x - 6
The Academic Support Center @ Daytona State College (Math, Page 16 of 19)
Graph using intercepts
2
5
y=- x-2
The Academic Support Center @ Daytona State College (Math, Page 17 of 19)
Interpreting the x and y intercepts
A trucking company purchases a new
truck for $75,000. The truck will
depreciate at $15,000 per year. The
equation that describes the
depreciation line is
y = 75,000 – 15,000x
Where y represents the value of the
truck and x is the age of the truck in
years.
1. What does the y-intercept
represent in the context of this
problem?
2. What does the x-intercept
represent in the context of this
problem?
y
70,000
60,000
50,000
40,000
30,000
20,000
10,000
1
2
Years
3
4
5
x
The Academic Support Center @ Daytona State College (Math, Page 18 of 19)
Graphing Exercise Handout
The Academic Support Center @ Daytona State College (Math, Page 19 of 19)