Chapter 2

Graphing and Writing Linear Equations

2.1 Graphing Linear Equations

Linear Equation

• An equation whose graph is a straight line.

• Anything with x to the first power

Solutions

• The points on the line

• Make the equation true

Determine if the ordered pair is a solution of the equation.

y = 2x + 1

(3 , 7 )

7 = 2(3) + 1YES

The ordered pair (3,7) is a solution.

Making a Table to Graph1. Solve for y: y=mx+b

2 . A. Pick your x values (-1, 0,1)

B. If “m” is a fraction and “b” is not then pick the + and – version of the denominator and 0 as your x -values

3. Plug in the x values into the equation to find the corresponding y values

4. Plot the (x, y) ordered pairs on the coordinate plane and draw a line

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10 x

yFind 3 solutions

y = 2x + 1

X Values Y=2x + 1 Y Values (x,y)

1

0

-1

2(1) +1 3 (1,3)

2(0) +1 1 (0,1)

2(-1) +1 -1 (-1,-1)

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10 x

yGraph:

x Y=2/3x +5 y (x,y)

3

0

-3

(2/3)(3) +5 7 (3,7)

(2/3) (0) +5 5 (0,5)

(2/3)(-3)+5 3 (-3,3)

25

3y x

Solve for ‘y’9 3 20x y

Solve for ‘y’ means “get y all by itself”

9x 9x3 9 20x y

203

3x y

3 3 3

8

6

4

2

-2

-4

-6

-8

-10 -5 5 10 x

yGraph:

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

X Y=2x +5 Y (x,y)

1

0

-1

2(1) +5 7 (1,7)

2(0) +5 5 (0,5)

2(-1)+5 3 (-1,3)

Types of Linear Lines

• Diagonal: when there are two variables

• Vertical: when there is only x

• Horizontal: when there is only y

Horizontal and Vertical Lines

• The graph of y= # is HORIZONTAL

• The graph x =# is VERTICAL

6

5

4

3

2

1

-1

-2

-3

-4

-5

-8 -6 -4 -2 2 4 6 8

Graph y = 4 using 3-points

x y

036

6

5

4

3

2

1

-1

-2

-3

-4

-5

-8 -6 -4 -2 2 4 6 8

Graph x = 6 using 3-points

x y

03

- 4

Homework

TB: Page 46 (2-18 even, 20-23 all, 24-32 even