Lesson 5-5 Standard 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 the y-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 fractions 2) 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. = 8and y-int. = 6 x=8y=6

You Try

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 graph of each equation? 1)x = 2 2)y = -5

Transforming to Standard Form

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