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Int. Alg. Notes Section 3.4 Page 1 of 3 Section 3.4: Linear Inequalities in Two Variables Big Idea: Sometimes you want to graph the situation where the outcome of a calculation involving two variables is greater than or less than a given number. For those cases, we need to learn how to graph linear inequalities in two variables to represent all the possible solutions. Big Skill: You should be able to graph a linear equation in two variables. Example of the type of problem we’ll learn to solve: If you purchase p pair of pants at $29.95 each and s shirts at $18.99 each, how many of each can you buy and not spend more than $120? Support Skill: Determining if an ordered pair satisfies a linear inequality Plug in the numbers and see if you get a true inequality. Practice: 1. Determine if (4, 1) is a solution of the linear inequality -2x + 3y 3. 2. Determine if (-1, 2) is a solution of the linear inequality -2x + 3y 3. 3. Determine if (0, 1) is a solution of the linear inequality -2x + 3y 3. Algebra is: the study of how to perform multi-step arithmetic calculations more efficiently, and the study of how to find the correct number to put into a multi-step calculation to get a desired answer. Int. Alg. Notes Section 3.4 Page 2 of 3 Main Skill: Graphing Linear Inequalities in Two Variables Step 1: Write the inequality as an equality, then graph the equation using a dashed line if it is a strict inequality (< or >), or using a solid line if it is not a strict inequality ( or ). Step 2: Pick a test point and see if the test point satisfies the inequality. If the test point satisfies the inequality, then shade the half of the plane containing the test point. If the test point does not satisfy the inequality, then shade the other half. Practice: 1. Graph the linear inequality y < -2x + 3. 2. Graph the linear inequality 6x – 3y 15. Algebra is: the study of how to perform multi-step arithmetic calculations more efficiently, and the study of how to find the correct number to put into a multi-step calculation to get a desired answer. Int. Alg. Notes Section 3.4 Page 3 of 3 3. If you purchase p pair of pants at $29.95 each and s shirts at $18.99 each, how many of each can you buy and not spend more than $120? To solve, write the problem as an inequality, graph it, then read off the ordered pairs. 4. If you are on a 1,500 calorie diet, and Wendy’s chicken breast filet has 430 calories, while a Frosty has 330 calories, how many of each can you eat and still maintain your diet? Algebra is: the study of how to perform multi-step arithmetic calculations more efficiently, and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.