5-6 Graphing Linear Inequalities in the Coordinate Plane Goal: Graph a linear inequality in the coordinate plane. Eligible Content: A1.1.3.2.1 / A1.1.3.2.2

Vocabulary Slope Intercept Form – y = mx + b Slope – rise over run y-intercept – point that the graph crosses the y axis

Solutions any ordered pairs that work in the inequality. Any ordered pairs that are in the shaded area of the graph. Any ordered pairs on the graph of a solid line.

Determining if a point is a solution Is the point (0, 1) a solution to the inequality : 2x – 3y > -2 No Is the point (1, -3) a solution to the inequality : 4x + 2y < 1 Yes Is the point (-3, 6) a solution to the inequality : x + 4y > 21

Graphing an inequality Get y alone Plot the y-intercept Use the slope to find more points Draw the line If > or < line is dotted If ≥ or ≤ line is solid Shade one side of the line Test the point (0,0) to see if it is a solution.

Where to Shade Shade above the line (UP) if you see: y > or y ≥ Shade below the line (DOWN) if you see: y < or y ≤

Graph: 2x + 3y < 6 2x + 3y < 6 -2x -2x 3y < – 2x + 6 3 3 3 y < – x + 2 m = - b = 2 dotted line

Examples y ≥ -2x + 4 -3x + 2y < 8 4x + 2y > 16 2x – 3y ≥ -6

Graph y – 3x < 2. A. B. C. D.

Graph x + 2y  6. A. B. C. D.

Practice 2x + y < 5 -3x + 2y ≥ 8 4x – 2y < 10 x > 4 y ≤ 3

Homework Page 320 #12-22 even