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The Academic Support Center @ Daytona State College (Math, Page 1 of 19)
GRAPHING LINEAR EQUATIONS
T H E R E C T A N G U L A R C O O R D I N A T E S Y S T E M
The Academic Support Center @ Daytona State College (Math, Page 2 of 19)
Rectangular Coordinate System
Graphing on a line
Graphing on a coordinate plane
0
VS.
The Academic Support Center @ Daytona State College (Math, Page 3 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 4 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 5 of 19)
Rectangular Coordinate System
Give the coordinates of the ordered pairs.
The Academic Support Center @ Daytona State College (Math, Page 6 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)
(1, - 7
3)
(3, 12)
(1
2 , 6)
(0, - 5
2 )
The Academic Support Center @ Daytona State College (Math, Page 7 of 19)
Interpreting a Graph
2 4 6 8 Miles
20 10
50 40 30
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. 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?
x
y
$
The Academic Support Center @ Daytona State College (Math, Page 8 of 19)
Graphing Linear Equations
Making a Table of Values
x y
- 1
1
2
4x – y = 6
The Academic Support Center @ Daytona State College (Math, Page 9 of 19)
Graphing Linear Equations
Making a Table of Values
x y
3x + 2y = 6
The Academic Support Center @ Daytona State College (Math, Page 10 of 19)
Graphing Linear Equations
Making a Table of Values
x y
- 2y = 6
The Academic Support Center @ Daytona State College (Math, Page 11 of 19)
Graphing Linear Equations
Making a Table of Values
x y
5x = -15
The Academic Support Center @ Daytona State College (Math, Page 12 of 19)
Graphing Linear Equations
Making a Table of Values
x y
y = 𝟏
𝟐x - 3
The Academic Support Center @ Daytona State College (Math, Page 13 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 14 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 15 of 19)
Graphing using x and y
intercepts
x – intercept ( ) on the x axis
y – intercept ( ) on the y axis
The Academic Support Center @ Daytona State College (Math, Page 16 of 19)
Graph using intercepts
3y = -5x - 6
The Academic Support Center @ Daytona State College (Math, Page 17 of 19)
Graph using intercepts
y = - 2
5x - 2
The Academic Support Center @ Daytona State College (Math, Page 18 of 19)
Interpreting the x and y intercepts
1 2 3 4 5 Years
20,000 10,000
50,000 40,000 30,000
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?
x
y
70,000
60,000
The Academic Support Center @ Daytona State College (Math, Page 19 of 19)
Graphing Exercise Handout