In this lesson… We will write and graph linear inequalities

Sharon earns $8 an hour and a bonus of $24 each week. Write an equation describing Sharon’s weekly pay.

Complete the table: HoursProcessTotal Pay xy

Complete the table: HoursProcessTotal Pay 08(0) (1) (2) (3) x8x + 24y

An equation to describe the total weekly earnings in terms of the number of hours worked is… y = 8x + 24 The amount Sharon needs to pay all of her bills must be less than or equal to the amount she earns

An inequality to describe the amount Sharon needs to earn to pay her bills is … Graph this Inequality

Begin at the y-intercept hours Bills ($)

Find a 2 nd point with the slope hours Bills ($)

Connect the points with a line hours Bills ($)

Shade below the line hours Bills ($) The shaded region represents the the amounts Sharon can afford

Paul claims he can run 4 miles a day. He has already run 32 miles this month. An equation describing the total number of miles that Paul has run in terms of the days is y = 4x + 32

Paul’s coach insists he run more than 4 miles each day to prepare to run in a marathon. Write an inequality describing the total miles the coach wants Paul to run.

The inequality shows the total miles, y, is greater than 4x + 32 y > 4x + 32 Graph this inequality

First Graph the y-intercept days Total Miles

Graph a second point days Total Miles

Connect with a dotted line days Total Miles The points on the line are not included since Paul must jog MORE than the amounts on the line

Shade ABOVE the line days Total Miles The shaded region represents the miles Paul must run

The Student Council is purchasing T-shirts and Posters to sell for a school fundraiser Each T-Shirt costs $6 and each poster costs $2

The Student Council Sponsor says that they must keep their spending below $120 for this fundraiser If T is the number of T- shirts, then 6T is the cost for all the T-Shirts

If P is the number of posters, then 2P is the cost for all the posters Since they must spend less than $120, the inequality for this problem is… 6T + 2P < 120

To graph this inequality, we can use T and P intercepts 6T + 2P < 120 TP 0 0

To graph this inequality, we can use T and P intercepts 6T + 2P < 120 TP

Graph each ordered pair Posters TP T-Shirts 60 6T + 2P < 120

Connect with a dotted line Posters TP T-Shirts 60 6T + 2P < 120

Shade below the line Posters TP T-Shirts 60 6T + 2P < 120

The shaded region represents the numbers of T-Shirts and Posters the Student Council can afford Posters T-Shirts 60 Can they afford 15 T-Shirts and 30 posters?

Complete Activity 6d Write Linear Inequalities Graph Linear Inequalities Solve Problems using Linear Inequalities