Graphing Linear Inequalities in Two Variables. Graphing Linear Inequalities The graph of a linear...

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Graphing Linear Inequalities in Two Variables. Graphing Linear Inequalities The graph of a linear inequality in two variables is the graph of all solutions

Text of Graphing Linear Inequalities in Two Variables. Graphing Linear Inequalities The graph of a linear...

Slide 1

Graphing Linear Inequalities in Two Variables Slide 2 Graphing Linear Inequalities The graph of a linear inequality in two variables is the graph of all solutions of the inequality. GRAPHING A LINEAR INEQUALITY The graph of a linear inequality in two variables is a half-plane. To graph a linear inequality, follow these steps. 1 STEP 2 Graph the boundary line of the inequality. Use a dashed line for and a solid line for or. To decide which side of the boundary line to shade, test a point not on the boundary line to see whether it is a solution of the inequality. Then shade the appropriate half-plane. The boundary line of the inequality divides the coordinate plane into two half- planes: a shaded region which contains the points that are solutions of the inequality, and an unshaded region which contains the points that are not. Slide 3 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. *Notice the line is dashed Slide 4 Graphing a Linear Inequality Sketch a graph of y 3 *Notice the line is solid Slide 5 Some Helpful Hints If the sign is > or < the line is dashed If the sign is or the line will be solid When dealing with just x and y. If the sign > or the shading either goes up or to the right If the sign is < or the shading either goes down or to the left Slide 6 Graphing Linear Inequalities in One Variable Graph a) y < 2 and b) x 1 in a coordinate plane. SOLUTION Test the point (0, 0). Because (0, 0) is not a solution of the inequality, shade the half-plane below the line. Graph the boundary line y = 2. Use a dashed line because y < 2. Test the point (0, 0). Because (0, 0) is a solution of the inequality, shade the half- plane to the left of the line. Graph the boundary line x = 1. Use a solid line because x 1. Slide 7 Using What We Know Sketch a graph of x + y < 3 Step 1: Put into slope intercept form y