Pen Tool McGraw-Hill Ryerson Pre-Calculus 11 Chapter 9 Linear and Quadratic Inequalities Section 9.1: Linear Inequalities in Two Variables Click here to begin the lesson

Pen Tool 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. Chapter 9 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

Pen Tool Linear Inequalities Click here for the solution. The ordered pair (x, y) is a solution to a linear inequality if its coordinates satisfy the condition expressed by the inequality. Chapter 9 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. Graph the boundary line and plot the points on the graph. Then, shade the region that represents the inequality.

Pen Tool Graphing Linear Inequalities Chapter 9 Match the inequality to the appropriate graph of a boundary line below. Complete the graph of each inequality by shading the correct solution region. MatchShade

Pen Tool Click here for the solution. Chapter 9 a) Graphing a Linear Inequality Graph the following inequalities. Describe the steps required to graph the inequality.

Pen Tool Chapter 9 Match each inequality to its graph. Then, click on the graph to check the answer. Graphing a Linear Inequality

Pen Tool Linear Inequalities Write an inequality that represents each graph. Chapter (2, 4) (0, -2 ) 0 (0, 3) (2, -1) 0

Pen Tool Solve an Inequality Click here for the solution. 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. Chapter 9 Let h = kg of hamburger c = kg of chicken 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. Chicken Hamburger

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

Pen Tool Homework Assignment: Pgs 472 – 475: #s 1- 11, 13, 14, 16, 20

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

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

Pen Tool Solutions Slope of the line is. 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. 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. An example method for graphing an inequality would be: Go back to the question.

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

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