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