Solve for “y ” for each:

1.) 2x + y = 9 2.) -x = y + 3

3.) 2y – 4 = 3x 4.) 2 = y – ⅓x

5.) 7x – y = -8 6.) 3y – 1 = -3x

y = -2x + 9

y = ⅓x + 2

y = -x - 3

y = 7x + 8 3y = -3x + 1

+⅓x +⅓x

-2x -2x - 3 - 3

+4 +4

-7x -7x +1 +1

-y = -7x - 8

2y = 3x + 4

Again, solve for “y ”

1.) 2x + 2y = 10 2.) 6x – 3y = -3

3.) 2y – 7 = -x 4.) 15x + 5y = 20

y = -x + 5y = 2x + 1

y = -½x + 3.5 y = -3x + 4

- 2x - 2x

2y = -2x + 10Divide by 2

- 6x - 6x

-3y = -6x - 3Divide by -3

+ 7 + 7

2y = -1x + 7 Divide by 2

- 15x - 15x

5y = -15x + 20

Divide by 5

-3 -3 -3

3.3 Graphing Linear Equations

Linear EquationAn equation for which the

graph is a STRAIGHT line

NO FRACTIONS and NO LEADING NEGATIVES!!!

Linear Equation: an equation whose graph forms a line.

1143 yx

262 xxy

is linear.

is not.

In linear equations, all variables are taken to the first power.

Why?

What is a Linear Equation?

A linear equation is an equation whose graph is a LINE.

y

x

Linear

Not Linear

SolutionAny ordered pair of numbers that makes a

linear equation true.

FOR: y = x - 9

(9,0) IS ONE SOLUTION

Can you think of another solution?

Is (11,2)??

Is (-5,-14)??

Yes

Yes

INFINITE AMOUNT OF SOLUTIONS

(x,y)

Determine if the ordered pair given is a solution of

x + 2y = 5

1.) (1,2) 2.) (7,-3)

(1) + 2(2) = 5?? (7) + 2(-3) = 5??

YES NO

5 = 5 1 = 5

Steps to GRAPHING

1.) SOLVE FOR “y”

2.) MAKE A T-CHART

3.) GRAPH EACH ORDERED PAIR

4.) CONNECT THE DOTS TO DRAW THE LINE

Linear Equation

Example:

y = x + 3

GraphingFind solutions using table

y = x + 3

x y

-2

-1

0

1

2

3

x y

-2 1

-1 2

0 3

1 4

2 5

3 6

Create these ordered pairs

(-2,1) and (-1,2) and (0,3)

and (1,4) and (2,5) and (3,6)

GraphingGraph the points from the table

(-2,1) (-1,2) (0,3) (1,4) (2,5)

GraphingDraw a line to connect them

So by looking at this line we can assume that (5,8) is a solution?

What other points can we conclude is a solution???

y = x +3

Suppose you were asked to graph the solution set of the linear equation,

FIRST SOLVE FOR Y!!

Then creating a table of values.xy

x + y = 3-x -x

y = -x + 3

Use the x-values -2, -1, 0, 1, and 2

xy

-2 -1 0 1 2

5 4 3 2 1

With your table completed for three sets of values, you are ready to graph the line.

xy

-2 -1 0 1 2

5 4 3 2 1

y = -x + 3

Graphing a Linear Equation

How do we graph linear equations?

Let’s try this one: y = 3x – 2

Make a Table of values

x y

–2

–1

0

1

2

y = 3(–2) – 2 = –8

y = 3(–1) – 2 = –5

y = 3(0) – 2 = –2

y = 3(1) – 2 = 1

y = 3(2) – 2 = 4

–8

–5

–2

1

4

y

x

Graphing a Linear Equationy

x

How about another one!

Let’s try x – 2y = 6.

First Step:

Solve for y

x – 2y = 6

–2y = -x + 6

y = ½x - 3

Second Step: Make a t-chart

x y

–4

–2

0

2

4

-5

-4

-3

-2

-1

½(-4) – 3 = -5

½(-2) – 3 = -4

½(-0) – 3 = -3

Create a table of values for each equation, and graph it on grid paper:

1. 2.

3.

5 yx 72 yx

42 xy4. 1

21 xy

x y

-2 3

-1 4

0 5

1 6

2 7

3 8

y = x + 5

x y

-4 -1

-2 0

0 1

2 2

4 3

6 4

x y

-2 -8

-1 -6

0 -4

1 -2

2 0

3 2

x y

-2 11

-1 9

0 7

1 5

2 3

3 1

y =-2 x + 7

Try TheseMake a table for each function using x-

valuse -2, -1, 0, 1, 2, 3:1) y = 2x + 3 2) y = -x - 4

x y

-2 -1

-1 1

0 3

1 5

2 7

3 9

x y

-2 -2

-1 -3

0 -4

1 -5

2 -6

3 -7

Find some solutions of this linear equations

1.) -2x + y = -3

First Solve for y

y = 2x - 3x y

-1 -5

0 -3

1 -1

2 1

3 3

Use the x-values of-1, 0, 1, 2 and 3

Make a t-chart for this function:

1.) -4x + y = -1

Graph the function y = 3x -2

First make a t-chart

Graph the function: 4y – 2x = 8First solve for “y”

4y – 2x = 8 +2x +2x

4y = 2x + 84 4 4

y = ½x + 2 x y

-4 0

-2 1

0 2

2 3

4 4

6 5

Then use which x-values???

First solve for “y”

3x – 2y = 6-3x -3x

-2y = -3x + 6-2 -2 -2

y = 3/2 x - 3 x y

-4 -9

-2 -6

0 -3

2 0

4 3

6 6

Then use which x-values???

Graph the function: 3x – 2y = 6

Graph the equationy = 2x + 6

X Y = 2x + 6 Y (x, y)

1 2(1) + 6 8 (1, 8) 2 2(2) + 6 10 (2, 10) 3 2(3) + 6 12 (3, 12) 4 2(4) + 6 14 (4, 14) 5 2(5) + 6 16 (5, 16)

Plot (-2, -4), (0, 2) and (1, 5)

Then draw the line. Make sure your line covers the graph and has arrows on both ends. Be sure to use a ruler.

Graph the equation: -6x + 2y = 4

y = 3x + 2

Which ordered pair does NOT satisfy the equation 2x + y = 7?

Which ordered is a solution of the equation 5x – 3y = 17?

a.) (1,5)

b.) (3,2)

c.) (0,7)

d.) (4,-1)

a.) (4,1)

b.) (1,4)

c.) (5,1)

d.) (1,5)