Graphing Linear Inequalities in 2 Variables

Checking Solutions 3x + 2y ≥ 2 An ordered pair (x,y) is a solution if it makes the inequality true. Are the following solutions to: 3x + 2y ≥ 2 (0,0) (2,-1) (0,2) 3(0) + 2(2) ≥ 2 4 ≥ 2 Is a solution 3(0) + 2(0) ≥ 2 0 ≥ 2 Not a solution 3(2) + 2(-1) ≥ 2 4 ≥ 2 Is a solution

To sketch the graph of a linear inequality: Sketch the line given by the corresponding equation (solid if ≥ or ≤, dashed if < or >). This line separates the coordinate plane into 2 half-planes. 2. In one half-plane – all of the points are solutions of the inequality. In the other half-plane - no point is a solution 3. You can decide whether the points in an entire half-plane satisfy the inequality by testing ONE point in the half-plane. 4. Shade the half-plane that has the solutions to the inequality.

Graphing an Inequality in Two Variables Graph x < 2 Step 1: Start by graphing the line x = 2 Now what points would give you less than 2? Since it has to be x < 2 we shade everything to the left of the line.

Graphing a Linear Inequality Sketch a graph of y  3

Step 1: Put into slope intercept form Using What We Know Sketch a graph of x + y < 3 Step 1: Put into slope intercept form y <-x + 3 Step 2: Graph the line y = -x + 3

The graph of an inequality is the graph of all the solutions of the inequality 3x+ 2y ≥ 2 y ≥ -3/2x + 1 (put into slope-intercept form to graph easier) Graph the line that is the boundary. Before you connect the dots check to see if the line should be solid or dashed solid if ≥ or ≤ dashed if < or >

y ≥ -3/2x + 1 Step 1: graph the boundary (the line is solid ≥) Step 2: test a point NOT On the line (0,0) is always The easiest if it’s Not on the line!! 3(0) + 2(0) ≥ 2 0 ≥ 2 Not a solution So shade the other side of the line!!

Graph: y < 6

y < 3x - 2

4x – 2y < 7