Graphing Linear Inequalities in Two Variables Objective: Graph all of the solutions to a linear inequality

Steps to Remember 1. Rewrite the inequality so that it is in slope-intercept form  y = mx + b 2. Plot the y-intercept (b) 3. Use the slope (m) to find other points on the line. 4. Draw the line  Solid if =  Dotted if  Dotted if 5. Shade above or below the line  Above if > or >=  Below if < or <=

Example 1 Graph y > 2x -5 The equation is already in slope- intercept form. Start by plotting the y-intercept (b = - 5)

Example 1 (cont) Graph y > 2x -5 Now use the slope to find other points on the line

Example 1 (cont) Graph y > 2x -5 Draw a dotted or solid line through the coordinates. This line will be dotted since the inequality is >

Example 1 (cont) Graph y > 2x -5 Shade above the line to show all of the coordinates that are solutions.

Example 2 Graph 2x - 5y >=15 First, solve for y … -5y >= -2x + 15 y <= 2/5 x – 3 Now go through the steps of graphing.

Example 2 Graph 2x - 5y >=15 y <= 2/5 x – 3 Plot the y-intercept

Example 2 Graph 2x - 5y >15 y <= 2/5 x – 3 Use the slope to find other points

Example 2 Graph 2x - 5y >15 y <= 2/5 x – 3 Draw a solid line through the points.

Example 2 Graph 2x - 5y >15 y <= 2/5 x – 3 Shade below the line

Special Example  Graph x > 5  Remember the graph will be a vertical line.

Special Example  Graph y< -2  Remember the graph will be a horizontal line.