Section 4.5

Graphing Linear Equations

The standard form of an linear equation is:

Ax + By = C

Where A> 0, A and B are not both zero,

and A, B, and C are integers whose greatest common factor is 1.

Linear Equation – An equation whose graph is a straight line

The standard form can can also be written in y –intercept form (and vice-versa):

y = mx + b

Where y must have a coefficient of +1.

For example:

Standard Form: Ax + By = C

6x + y = 7

-6x -6x

y = -6x + 7

y –intercept form: y = mx + b

For example:

Standard Form: Ax + By = C

5x - y = 10

-5x -5x

-y = -5x + 10

y –intercept form: y = mx + b

y = 5x - 10

Rewrite the following to standard form

Ax + By = C:

y = -2x + 5

2x + y = 5

y = 2x y = -3x + 5 y = 3x - 4

y = 2x2 – 3 y = x2 y = (x+3)2

y = 2x -5 y = 2x3 y = -4x -5

y = 3x2 y = x3-2 y = 2x + 6

y = -2x x = y y = x4 + 3

y = 10x + 3 (x -3)2 = y x – 100 = y

y = x2 + 3 y – 1 = 1/2x 4y = 8x + 20

5 = 2x - y 3y = 9x -3 5x4 -5 = y

Linear Equation – An equation whose graph is a straight line

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Graphing Equations using tables: The Five Steps

y = 3x

x 3x y

-2 3(-2) -6

-1 3(-1) -3

0 3(0) 0

1 3(1) 3

2 3(2) 6

y = 2x

x y-2 -4

-1 -2

0 0

1 2

2 4

-2x + y = 5

y = 2x + 5

x 2x+5 y

-2 2(-2)+5 1

-1 2(-1)+5 3

0 2(0)+5 5

1 2(1)+5 7

2 2(2)+5 9

Homework:

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