Section 2 8 Graphing Linear Inequalities A linear

Section 2. 8: Graphing Linear Inequalities

A linear inequality resembles a linear equation, but with an inequality instead of an equals symbol. For example, y > – 3 x – 2 versus y = – 3 x – 2. • The graph of the inequality y > – 3 x – 2 is shown at the right as a shaded region. • Every point in the shaded region satisfies the inequality. The graph of y = – 3 x – 2 is the boundary of the region. It is drawn as a dashed line to show that points on the line do not satisfy the inequality. If the symbol was ≤ or ≥, then the points on the boundary would satisfy the inequality, so the boundary would be written as a solid line.

• Example 1: Graph x – 2 y < 4.

• Example 2: One tutoring company advertises that it specializes in helping students who have a combined score on the SAT that is 900 or less. • a) Write an inequality to describe the combined scores of students who are prospective tutoring clients. Let x represent the verbal score and y the math score. Graph the inequality. • b) Does a student with verbal score of 480 and a math score of 410 fit the tutoring company’s guidelines?

• Example 3: Two social studies classes are going on a field trip. The teachers have asked for parent volunteers to also go on the trip as chaperones. However, there is only enough seating for 60 people on the bus. • a) What is an inequality to describe the number of students and chaperones that can ride on the bus? • a) s + c ≥ 60 • c) s + c < 60 b) s + c ≤ 60 d) s + c > 60

• b) Can 15 chaperones and 47 students ride on the bus?