Welcome to class! Have a great day! I ll miss you while I m gone :)

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Samuel Mosley
5 years ago
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1 Welcome to class! 1. You have a substitute (Ms. Williams) today while I am at training for Nonviolent Crisis Intervention. I have very high expectations for you in my absence 2. I know I didn t put the desks back. You may choose your seat, but make smart choices that won t get you into trouble. 3. Today s lesson has already been posted on my website under the notes section. It is self paced/self guided. You should open it on your chromebook and take notes. You can raise your hand and ask Ms. Williams if you need help. 4. If you finish early, you may start your homework. 5. I will check notes AND homework tomorrow, so don t skip the notes and jump straight to the homework. Have a great day! I ll miss you while I m gone :)

2 Graphing Linear Inequalities 12/7/2017

3 Warm-Up Solve the following inequalities for y: 5x - 2y > 4 3x < y - 2

4 Warm-Up Answers Solve the following inequalities for y: 5x - 2y > 4 y < /2 x 3x < y - 2 3x + 2 < y Don t forget!!! We flip the inequality if we multiply or divide both sides by a negative!

5 After today s lesson you should be able to... Identify solutions of linear inequalities Graph an inequality with 2 variables Graph an inequality with 1 variable Write and graph an inequality from a word problem Write an inequality from a graph

6 Linear Inequalities Linear Inequality: An inequality in two variables whose graph is a region of the coordinate plane that is bounded by a line. Each point in the region is a solution of the inequality Example: y > 3x + 2

7 Linear Inequalities Linear Inequality: An inequality in two variables whose graph is a region of the coordinate plane that is bounded by a line. Each point in the region is a solution of the inequality A linear inequality in two variables has an infinite number of solutions. These solutions can be represented in the coordinate plane as the set of all points on one side of a boundary line.

8 Linear Inequalities Linear Inequality: An inequality in two variables whose graph is a region of the coordinate plane that is bounded by a line. Each point in the region is a solution of the inequality A linear inequality in two variables has an infinite number of solutions. These solutions can be represented in the coordinate plane as the set of all points on one side of a boundary line. All points on one side of the boundary line are solutions, while the other side are not solutions

9 Answer: Yes! (1,2) is a solution of y > x-3 Example You Try

10 y > x - 3 Write the inequality -7 > -3-3 Substitute -7 > -6 X Simplify Answer: Yes! (1,2) is a solution of y > x-3 Answer: No! (-3, -7) is not a solution of y > x - 3 Example You Try

11 Graphing Rules > or < Graph with a dashed line > or < Graph with solid line < or < shade below the line > or > shade above the line

12 Dashed vs. Solid Lines & Shading Shade below because of the > Shade above because of the >

13 FYI The shading represents where possible solutions to your inequality exist. In other words, every single point in the shaded area should create a true inequality if you plugged them in. Likewise, points in the non-shaded region would not create true inequalities if you plugged them in. If the line is solid, it means those would work if you plugged them in. If it is dashed, it means they would not work.

Use a dashed line to show that the points are not included in the solution The direction of the inequality symbol determines which side of the boundary line to shade.

14 Use a dashed line to show that the points are not included in the solution The direction of the inequality symbol determines which side of the boundary line to shade. If the symbol is or, shade below the boundary line. If the symbol is or, shade above it. Sorry my shading looks terrible - I had to draw it with my mouse I would normally use highlighter

15 What is the graph of y > x - 2? First: graph the boundary line y = x - 2. (Since the inequality is >, the point on the boundary line are not solutions.

16 What is the graph of y > x - 2? First: graph the boundary line y = x - 2. (Since the inequality is >, the point on the boundary line are not solutions.

17 What is the graph of y > x - 2? First: graph the boundary line y = x - 2. (Since the inequality is >, the point on the boundary line are not solutions. Second: To determine which side of the boundary line to shade, test a point that is not on the line.

18 What is the graph of y > x - 2? First: graph the boundary line y = x - 2. (Since the inequality is >, the point on the boundary line are not solutions. Second: To determine which side of the boundary line to shade, test a point that is not on the line. Plug (0,0) into my inequality 0 > > -2 Because this IS a solution, I need to shade on the side where (0,0) is.

19 What is the graph of y > x - 2? First: graph the boundary line y = x - 2. (Since the inequality is >, the point on the boundary line are not solutions. Second: To determine which side of the boundary line to shade, test a point that is not on the line. Plug (0,0) into my inequality 0 > > -2 Because this IS a solution, I need to shade on the side where (0,0) is. Sorry my shading looks terrible - I had to draw it with my mouse I would normally use highlighter

20 What is the graph of y > x - 2? First: graph the boundary line y = x - 2. (Since the inequality is >, the point the boundary The shaded region line are not solutions. represents ALL ordered pairs that would be TRUE for the inequality!!! Second: To determine which side of the boundary line to shade, test a point that is not on the line. Plug (0,0) into my inequality 0 > > -2 Because this IS a solution, I need to shade on the side where (0,0) is. Sorry my shading looks terrible - I had to draw it with my mouse I would normally use highlighter

21 Graph the following

22 Graph the following Solid line Shade below

Dotted line because it s not equal to -1, just greater than -1. Shade to the right because everything to the right of -1 is where x is bigger than -1. Solid line because it can be equal to 6.

24 Dotted line because it s not equal to -1, just greater than -1. Shade to the right because everything to the right of -1 is where x is bigger than -1. Solid line because it can be equal to 6. Shade to the left because everything to the left of 6 is where x is smaller than 6. Dotted line because it s not equal to -4, just greater than -1. Shade above because everything above -4 is where y is bigger than -4. Solid line because it can be equal to 2. Shade below because everything below 2 is where y is smaller than 2.

26 x y peanuts cashews 12 > 2x + 4y 12 > 2x + 4y 12-2x > 4y 3 - ½ x > y (0, 0) 0 peanuts, 0 cashews (1, 2) 1 peanuts, 2 cashews (2, 1) 2 peanuts, 2 cashews

27 x y peanuts cashews 12 > 2x + 4y 12 > 2x + 4y Any ordered pair in the 12-2x > 4y shaded region including on the line is a possibility! 3 - ½ x > y Except would (-2, -5) make sense? No not really so we still need to critically (0, 0) 0 peanuts, think 0 cashews about our answer in (1, 2) 1 peanuts, context 2 cashews (2, 1) 2 peanuts, 2 cashews

28 Write an inequality from a graph

29 Write an inequality from a graph The boundary line is y = 2x + 1 The answer is y < 2x + 1 It s less than because it s shaded below the line It s equal to because it s a solid line.

30 After today s lesson you should be able to... Identify solutions of linear inequalities Graph an inequality with 2 variables Graph an inequality with 1 variable Write and graph an inequality from a word problem Write an inequality from a graph FYI, we will quickly review all of this when I return tomorrow, so if it didn t sink in the first time, don t worry! I got you.

31 Homework Page 394 # 11-16, 24-28, 30-33, 42

Hot X: Algebra Exposed

Hot X: Algebra Exposed Solution Guide for Chapter 10 Here are the solutions for the Doing the Math exercises in Hot X: Algebra Exposed! DTM from p.137-138 2. To see if the point is on the line, let s plug