Chapter 3 Graphs and Functions Copyright 2015 2011

Chapter 3 Graphs and Functions Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -

Chapter Sections 3. 1 – Graphs 3. 2 – Functions 3. 3 – Linear Functions: Graphs and Applications 3. 4 – The Slope-Intercept Form of a Linear Equation 3. 5 – The Point-Slope Form of a Linear Equation 3. 6 – The Algebra of Functions 3. 7 – Graphing Linear Inequalities Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -2 2

§ 3. 7 Graphing Linear Inequalities Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -

Graph Linear Inequalities Linear Inequality in Two Variables A linear inequality in two variables can be written in one of the following forms: ax + by < c, ax + by > c, ax + by ≤ c, ax + by ≥ c where a, b, and c are real numbers and a and b are not both 0. Examples: 2 x + 3 y > 2 -x – 2 y ≤ 3 3 y < 4 x - 9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -4 4

Graph Linear Inequalities Consider the graph of the equation x + y = 3. The line acts as a boundary between two half-planes and divides the plane into three distinct sets of points. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -5 5

Graph Linear Inequalities 1. 2. 3. To get the equation of the boundary line, replace the inequality symbol with an equals sign. Draw the graph of the equation in step 1. If the original inequality contains a or symbol, draw the boundary line using a solid line. If the original inequality contains a < or > symbol, draw the boundary line using a dashed line. Select any point not on the boundary line and determine if this point is a solution to the original inequality. If the point selected is a solution, shade the half-plane on the side of the line containing this point. If the selected point does not satisfy the inequality, shade the halfplane on the side of the line not containing the point. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -6 6

Graph Linear Inequalities Graph y < 2 x + 1. dashed line Checkpoint (0, 0 ) satisfies the inequality. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 3 -7 7