Section 2.2

Graphing Linear Equations

Solutions of Equations in Two Variables

Graphing from a Table of Points

Graphing from the Intercepts

Horizontal & Vertical Lines

Linear Models

Solutions to Equations

A solution to an equation in two variables is any

ordered pair of numbers (a,b) that makes a true

statement when substituted into the equation.

Example: (2,7) is a solution to y = 3x + 1

because 7 = 3(2) + 1

You can find solutions by choosing a value for one

variable, then solving the equation for the other variable

Example: For y = 3x + 1 Let x = 9

then y = 3(9) + 1 = 28

and this solution is shown by (9,28)

Class Exercise – Finding Solutions

a.) What is the solution

when x = 6 ?

b.) What is the solution

when y = 5 ?

53

1 xy

3

52

563

1

y

y

y

x

x

x

0

3

10

55

53

15

Why graph equations?

Consider the equation with two variables,

What will the solutions for this equation look like?

Ordered pairs: (x-value, y-value) (0,-3) for example

How many solutions are there?

Infinitely many

32 xy

Definitions

• The graph of an equation

is the set of all points (x, y) on the rectangular

coordinate system whose coordinates satisfy the

equation. It is the visual solution set for the equation.

• A linear equation in two variables

is an equation that can be put into the form Ax+By=C

(A and B can’t both be zero).

The graph of a linear equation is always a line.

Rough Graphing

Plan to use about

1/6 of a sheet

of paper

Neatly draw the

x-axis and y-axis

Label every 5 units

-15 -10 -5 0 5 10 15

15

10

5

-5

-10

-15

Class Exercise – Graphing an Equation

You already found two points: (6,3) and (0,5)

Find another point when x = -3

Use these 3 points to rough graph the equation

53

1 xy

Graphing using

The Intercept Method (“Cover-up Method”)

The y-intercept of a line is the point (0, b), where

the line intersects the y-axis.

To find b, substitute 0 for x in the equation of the line and

solve for y.

The x-intercept of a line is the point (a, 0), where

the line intersects the x-axis.

To find a, substitute 0 for y in the equation of the line and

solve for x.

Another Example: 7x – 14y = 35

53

1 xy

In-Class Exercises:

Make a table of 3 points and use it to graph

Graph using intercepts:

2

5

2

1 xy

1234 yx

How would you graph the following

equations?

3y

2x

Horizontal & Vertical Lines Is y = 3 a Linear Equation?

0x + y = 3 Yes!

Is x = 2 a Linear Equation?

x + 0y = 2 Yes!

Graph: x = -5 y=-4 y = 0

Horizontal and Vertical Lines

If a is any real number:

The graph of x = a is a vertical line with x-intercept (a, 0)

If a is 0, ( x = 0 ) the line is the y-axis.

If b is any real number:

The graph of y = b is a horizontal line with y-intercept (0, b)

If b is 0, ( y = 0 ) the line is the x-axis.

Linear Models We can use linear equations to mathematically model some real-life

situations. This way we can use observations about what happened in the

past to predict what might take place in the future.

Exercise56. TELEPHONE COSTS

In a community, the monthly cost of local telephone serviceis $5 per month, plus 25¢ per call.

a.Write a linear equation that gives the cost c for a. person making n calls.

b. Then graph the equation. (need 2 points)

c. Use the graph to estimate the cost of service in a month when 20 calls were made.

c = 5 + .25n

(0,?) -> (0,5)

(10,?) -> (10,7.5)

What Next?

Present Section 2.3

Rate of Change & Slope of a Line

Accessing these Powerpoint Slides from the Internet:

http://faculty.rcc.edu/vandewater/Section02_2.ppt

Click on Open