Graphing Linear Inequalities in Two Variables
Learn how to graph solutions to linear inequalities in two variables with this easy-to-follow guide. Start by rewriting the inequality in slope-intercept form (y = mx + b), then plot the y-intercept. Use the slope to determine additional points and draw the line. Remember to use a solid line for ≥ or ≤ and a dotted line for > or
Graphing Linear Inequalities in Two Variables
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Presentation Transcript
Graphing Linear Inequalities in Two Variables Objective: Graph all of the solutions to a linear inequality
Steps to Remember • Rewrite the inequality so that it is in slope-intercept form • y = mx + b • Plot the y-intercept (b) • Use the slope (m) to find other points on the line. • Draw the line • Solid if <= or >= • Dotted if < or > • 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.
