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In this lesson…

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:. Complete the table:.

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In this lesson…

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  1. In this lesson… We will write and graph linear inequalities

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

  3. Complete the table:

  4. Complete the table:

  5. 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

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

  7. Begin at the y-intercept Bills ($) 40 32 24 16 8 hours 1 2 3 4 5

  8. Find a 2nd point with the slope Bills ($) 40 32 24 16 8 hours 1 2 3 4 5

  9. Connect the points with a line Bills ($) 40 32 24 16 8 hours 1 2 3 4 5

  10. Shade below the line Bills ($) The shaded region represents the the amounts Sharon can afford 40 32 24 16 8 hours hours 1 2 3 4 5

  11. 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

  12. 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.

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

  14. First Graph the y-intercept Total Miles 40 36 32 24 16 12 8 4 days 1 2 3 4 5

  15. Graph a second point Total Miles 40 36 32 24 16 12 8 4 days 1 2 3 4 5

  16. Connect with a dotted line Total Miles The points on the line are not included since Paul must jog MORE than the amounts on the line 40 36 32 24 16 12 8 4 days 1 2 3 4 5

  17. Shade ABOVE the line Total Miles The shaded region represents the miles Paul must run 40 36 32 24 16 12 8 4 days 1 2 3 4 5

  18. 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

  19. 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

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

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

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

  23. Graph each ordered pair 6T + 2P < 120 Posters 60 50 40 30 20 10 T-Shirts 5 10 15 20 25

  24. Connect with a dotted line 6T + 2P < 120 Posters 60 50 40 30 20 10 T-Shirts 5 10 15 20 25

  25. Shade below the line 6T + 2P < 120 Posters 60 50 40 30 20 10 T-Shirts 5 10 15 20 25

  26. The shaded region represents the numbers of T-Shirts and Posters the Student Council can afford Posters 60 Can they afford 15 T-Shirts and 30 posters? 50 40 30 20 10 T-Shirts 5 10 15 20 25

  27. Complete Activity 6d • Write Linear Inequalities • Graph Linear Inequalities • Solve Problems using Linear Inequalities

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