Chapter 9 Linear and Quadratic Inequalities Section 9.1

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Raymond Burns
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1 McGraw-Hill Ryerson Pre-Calculus 11 Linear and Quadratic Inequalities Section.1 Click here to begin the lesson

Linear Inequalities The graph of the linear equation x y = 2 is referred to as a boundary line. This line divides the Cartesian plane into two regions: For one region, the condition x y < 2 is true.

2 Linear Inequalities The graph of the linear equation x y = 2 is referred to as a boundary line. This line divides the Cartesian plane into two regions: For one region, the condition x y < 2 is true. For the other region, the condition x y > 2 is true. Use the pen to label the conditions below to the corresponding parts of the graph on the Cartesian plane. x y < 2 x y = 2 x y < 2 x y > 2 x y > 2

3 Linear Inequalities The ordered pair (x, y) is a solution to a linear inequality if its coordinates satisfy the condition expressed by the inequality. Which of the following ordered pairs (x, y) are solutions of the linear inequality x 4y < 4? Click on the ordered pairs to check your answer , 2, , 2 Use the pen tool to graph the boundary line and plot the points on the graph. Then, shade the region that represents the inequality. 0,0 0,4 0, 4 4,0 4,0 x4y 4 Click here for the solution.

4 Graphing Linear Inequalities Match the inequality to the appropriate graph of a boundary line below. Complete the graph of each inequality by shading the correct solution region. Match Shade

5 Graphing a Linear Inequality Use the pen tool to graph the following inequalities. Describe the steps required to graph the inequality. a) Click here for the solution.

6 Graphing a Linear Inequality Match each inequality to its graph. Then, click on the graph to check the answer.

7 Linear Inequalities Write an inequality that represents each graph (0, 3) (2, 4) 0 (2, -1) 0 (0, -2) 2xy 3 3xy 2

8 Chicken Let h = kg of hamburger c = kg of chicken Solve an Inequality Paul is hosting a barbecue and has decided to budget $48 to purchase meat. Hamburger costs $5 per kilogram and chicken costs $6.50 per kilogram. Write an inequality to represent the number of kilograms of each that Paul may purchase. Write the equation of the boundary line below and draw its graph. Shade the solution region for the inequality. Hamburger Click here for the solution.

9 Chicken Solve an Inequality c 5h6.5c48 h Hamburger 1. Can Paul buy 6 kg of hamburger and 4 kg chicken if he wants to stay within his set budget? No 2. How many kilograms of chicken can Paul buy if he decides not to buy any hamburger? 7.38 kg 3. If Paul buys 3 kg of hamburger, what is the greatest number of kilograms of chicken he can buy? 5.08 kg Click here for the solution.

10 For next class complete the following: p. 472, #1 a, #2a, #3 c, e, #4 a, b, #, p. 473, #17

11 The following pages contain solutions for the previous questions. Click here to return to the start

12 Solutions (0, 4) 0 (-4, 0) (0, 0) (4, 0) (0, -4) Go back to the question.

Therefore, shade below the line. 1 The x-intercept is the point ( 2, 0), the y-intercept is the point (0, 4).

13 Solutions An example method for graphing an inequality would be: Slope of the line is 3. and the y-intercept is the point (0, 1). The inequality is less than. Therefore, the boundary line is a broken line. Use a test point (0, 0). The point makes the inequality true. Therefore, shade below the line. 1 The x-intercept is the point ( 2, 0), the y-intercept is the point (0, 4). The inequality is greater than and equal to. Therefore, the boundary line is a solid line. Use a test point (0, 0). The point makes the inequality true. Therefore, shade above the line. Go back to the question.

kilograms of each that Paul may purchase.

14 Chicken Solutions Let h = kg of hamburger c = kg of chicken c Write an inequality to represent the number of kilograms of each that Paul may purchase. Graph the boundary line for the inequality. h Hamburger Go back to the question.

15 Chicken Solutions c (0, 7.38) (3, 5) 5h6.5c48 (6, 4) h Hamburger 1. Can Paul buy 6 kg of hamburger and 4 kg chicken if he wants to stay within his set budget? The point (6, 4) is not within the shaded region. Paul could not purchase 6 kg of hamburger and 4 kg of chicken. 2. How many kilograms of chicken can Paul buy if he decides not to buy any hamburger? This is the point (0, 7.38). Buying no hamburger would be the y-intercept of the graph. 3. If Paul buys 3 kg of hamburger, what is the greatest whole number of kilograms of chicken he can buy? This would be the point (3, 5). Paul could buy 5 kg of chicken. Go back to the question.

MA 1128: Lecture 08 03/02/2018. Linear Equations from Graphs And Linear Inequalities

MA 1128: Lecture 08 03/02/2018 Linear Equations from Graphs And Linear Inequalities Linear Equations from Graphs Given a line, we would like to be able to come up with an equation for it. I ll go over