SOLVING & GRAPHING

LINEAR EQUATIONS•Determine if an equation is linear

•Identify the domain and range USE YOUR CALCULATOR TO:

•Find the domain when given the range•Find the range when given the domain

•Graph linear equations and inequalities.

To determine if an equation is LINEAR it must have a degree of ONE

How do you find DEGREE? Add the exponents of

the variables for each monomial.

5x + 2y = 7 3x2 + 2y = 4 1/x – 1/y = 2 3/5x = y 3/5 x = y y/2 = 2

•What is ANY line that you graph made up of?

•A series of POINTS

•In this lesson, we are going to find those points and use them to graph the line.

BEFORE GRAPHING…….. CHECK YOUR CALCULATOR SETTINGS! CHECK WINDOW SETTINGS.

Press ZOOM at the top of the calculator Choose option #6 ZStandard – this will give you a

“standard” 10 x 10 window. NEXT CHECK PLOTS.

Press Y= At the top of the graph, Plot1, Plot2, Plot3 should

NOT be highlighted. If the are, arrow up and press enter then arrow back down to Y1. This will turn them off.

Solve each equation for the given domain, then graph.

1. 2x – y = -3 if the domain is {-3, -1, 0, 1, 3}x y

-3

-1

0

1

3

FIRST – Solve for “y”

2 3x y

domain range

2x 2x2 3y x 12 3y x

Select y= button on your calculator. Type equation into line labeled “Y1”

“X” is located under 2nd, next to “alpha” Press 2nd then GRAPH Choose your answer from the appropriate column.

Use arrow keys to scroll up and down to find numbers.

-3 1 3 5 9

List ordered pairs from the table. (-3, -3) (-1, 1) (0, 3) (1, 5) (3, 9)

Graph the ordered pairs

Now press “GRAPH” on the calc. to see if the lines match.

Graph

Solve each equation for the given domain, then graph.2. 2x – 3y = 12 if

the range is {-6, -4, -2, 0, 4}x y

-6-4-204

FIRST – Solve for “y”

2 3 12x y

domain range

2x 2x3 2 12y x

324

3y x

Select y= button on your calculator. Type equation into line labeled “Y1”

“X” is located under 2nd, next to “alpha” Press 2nd then GRAPH Choose your answer from the appropriate column.

Use arrow keys to scroll up and down to find numbers.

-3 0 3 6

12

Example 2

List ordered pairs from the table. (-3, -6) (0, - 4) (3, -2) (6, 0) (12, 4)

Graph the ordered pairs

Now press “GRAPH” on your calc. to see if the lines match.

Graph 2

Name the domain OR the range, then graph the equation.

3. 3x + y = -6

x y

6-2

-30

-9

FIRST – Solve for “y”

3 6x y

domain range

3x 3x3 6y x

Select y= button on your calculator. Type equation into line labeled “Y1”

“X” is located under 2nd, next to “alpha” Press 2nd then GRAPH Choose your answer from the appropriate column.

Use arrow keys to scroll up and down to find numbers.

-4 0

-1 -

6 1

Example 3

List ordered pairs from the table. (-4, 6) (-2, 0) (-1, -3) (0, -6) (1, -9)

Graph the ordered pairs

Now press “GRAPH” on the calc. to see if the lines match.

Graph 3

What about INEQUALITIES?

Work everything exactly the same way.

Pay attention to your inequality symbol when you are graphing. > draw a - - - - - - - - - < draw a - - - - - - - - - > draw a ___________ < draw a ___________

The Inequality symbols tell you which side of the line to shade. < and < tell you to

shade BELOW the graphed line (the part BELOW where it crosses the y-axis.

> and > tell you to shade ABOVE the graphed line (the part ABOVE where it crosses the y-axis.

Let’s look at the graphs for #1 and #2

2 3y x * The symbol is < so that means to shade BELOW the line you graphed – below where it crosses the “y”-axis.

Y-intercept

< or > use ___________

24

3y x

* The symbol is > so that means to shade ABOVE the line you graphed – above where it crosses the “y”-axis.

< or > use - - - - - - - -

Y-intercept

Graph