Warm ups (HW will get stamped tomorrow)

Complete the given ordered pairs of the following equation: y = 4x + 2

(-3,?) (?,0) (4,?) (?,5)

5-4 Graphing Linear Equations

Objective: To identify a linear equation and graph linear

equations.

Graphing Linear equations… Without a domain!! Dun dun dunn….

What if we don’t give you the domain? How will you pick good numbers?

Solve for y Logic – pick whole #s At least 3 points

Why?

Example 1

Graph y = 3x – 1

x y

Example 2

Graph y = 1x – 4 2

x y

Example 3

Graph x + 2y = 6

x y

2 Special CasesOnly x

x + 2 = -3

x = -5

(-5, __)

You can plug in any number for y, x will always be -5. Vertical line!!

Only y

2y = 8

y = 4

(__, 4)

You can plug in any number for x, y will always be 4. Horizontal line!!

Linear equation:

Something that can be written in standard form Ax + By = C

A is always positive

Change to Ax + By = C Standard Form

4x = 7 + 2y

-2y - 2y

4x – 2y = 7

y = 4x – 1

-4x -4x

-4x + y = -1

-1(-4x + y = -1)

4x – y = 1

TOO

1. x + 3 = 2y + 5 2. y + 10 = 5 3. 5x + 2x = y - 5

x – 2y = 2 y = -5 7x – y = -5

Not Linear Equations

An equation is not linear if:

1. The variable has an exponent

3x2 – 4y = 0

2. The variable is in the denominator of a fraction 3 + 4y = 4 x3. The variables are being multiplied together

3xy = 4

Linear Equations

Is it a linear equation? If so, write in standard form. If not, why? No:

Denominator

Exponent

multiply

1. 3 + y = 2 x 4

2. x - 2y = 5 5

3. 3y + 2 = 0 4. 8x - 7y = 2x - 5

5. 4x2 – 3x = y 6. 5xy = 30

Homework

Pg. 283 # 16-27, 29, 32, 35, 36, 37, 42