Lesson 5-5Standard Form

Sept. 24, 2014

Daily Learning Target

• I will write and graph equations in standard form.

Intercepts

• Think about what the word “intercept” means.

• What does they-intercept look like?• What does the x-intercept look like?

Standard Form• Any linear equation can be expressed in the form Ax + By

= C where A, B, and C are integers and A and B are not both zero. This is called standard form. An equation that is written in point-slope form can be written in standard form.

• Rules for Standard Form:• Standard form is Ax + By = C, with the following

conditions:1) No fractions2) A is not negative (it can be zero, but it can't be negative).

By the way, "integer" means no fractions, no decimals. Just clean whole numbers (or their negatives).

Example 1

• Find the x- and y-intercepts of the graph of 3x + 4y = 24

We will substitute 0 for the x and y (at different times) to identify the intercepts.

x-int. = 8 and y-int. = 6x=8 y=6

You Try

• What are the x- and y-intercepts of the graph of each equation.

1) 5x – 6y = 60x = 12; y = -102) 3x + 8y = 12x = 4; y =

Example 2

• What is the graph of x – 2y = -2• Find the x- and y-intercepts.x = -2; y = 1• Graph each intercept and connect the points

You Try

• What is the graph of 2x + 5y = 10?

Graphing Horizontal and Vertical Lines

• What is the graph of each equation?1) x = 3

2) y = 3

You Try

• What is the graphof each equation?

1) x = 2

2) y = -5

Transforming to Standard Form

• What is y = - + 5 written in standard form?• Step 1: Get rid of the fraction (distributive

property)• Step 2: Get the x and y on the same side of the

equal sign.

Transforming to Standard Form

• Write y – 2 = - (x + 6)• Step 1: Simplify to get rid of the parenthesis• Step 2: Get rid of the fraction• Step 3: Rearrange the equation to put x and y

on the same side.

Model

• The iTunes store sells songs for $1 each and movies for $12 each. You have $60 to spend. Write and graph an equation that describes the items you can purchase. What are three combinations of numbers of songs and movies you can purchase?

You Try

• In the last example, suppose the store changed the price of movies to $15 each. What equation describes the number of songs and movies you can purchase for $60.

• What domain and range are reasonable for the above equation? Explain.

Homework

• Workbook• Page 155 problems 3, 5, 6, 8, 9, 10-12, 17, 20• Page 157 problems 1-5