Chapter 3 Graphs and Functions

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 Chapter 1 Outline

Graphing Linear Inequalities § 3.7 Graphing Linear Inequalities

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: 2x + 3y > 2 -x – 2y ≤ 3 3y < 4x - 9

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.

Graph Linear Inequalities 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 half-plane on the side of the line not containing the point.

Graph Linear Inequalities Graph y < 2x + 1. dashed line Checkpoint (0, 0 ) satisfies the inequality.