Graphing Linear Inequalities in Two Variables Checking Solutions
Graphing Linear Inequalities in Two Variables
Checking Solutions • An ordered pair (x, y) is a solution if it makes the inequality true. • Are the following solutions to: • 3 x + 2 y ≥ 2 • (0, 0) 3(0) + 2(0) ≥ 2 0≥ 2 Not a solution (2, -1) 3(2) + 2(-1) ≥ 2 4≥ 2 Is a solution (0, 2) 3(0) + 2(2) ≥ 2 4≥ 2 Is a solution
To sketch the graph of a linear inequality: 1. 2. Sketch the line given by the corresponding equation (solid if ≥ or ≤, dashed if < or >). This line separates the coordinate plane into 2 half-planes. In one half-plane – all of the points are solutions of the inequality. In the other half-plane - no point is a solution TRUE Shade that half!!! If FALSE shade the other half
The graph of an inequality is the graph of all the solutions of the inequality • 3 x+ 2 y ≥ 2 • y ≥ -3/2 x + 1 • • (put into slope intercept to graph easier) Graph the line that is the boundary of 2 half planes Before you connect the dots check to see if the line should be solid or dashed solid if ≥ or ≤ dashed if < or >
y ≥ -3/2 x + 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!!
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.
Sketch a graph of y 3
6 4 2 5
6 4 2 5
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