M1410705 - (Sections 7.5-7.6: Graphing Inequalities and...

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(Sections 7.5-7.6: Graphing Inequalities and Linear Programming) 7.36 SECTION 7.5: GRAPHING INEQUALITIES, and SECTION 7.6: LINEAR PROGRAMMING In Example 2 on p.542 , the one-variable linear inequalities x > 2 and y 3 are graphed in the xy -plane. In Example 3 on p.542 , the two-variable linear inequality x y < 2 is graphed in the xy -plane. Two methods: Method 1: Test Point Method Step 1: Graph the boundary line, which separates the xy -plane into two half- planes. • Replace the inequality symbol with “=” to obtain the equation of the boundary line. • To figure out how to graph the line, § Put the equation in slope-intercept form: y = mx + b , or § Plot the intercepts. (See Section 1.3: Notes 1.16-1.17 .) If the inequality had Then graph the line as or (weak inequality) a solid line (We include the line in the graph.) < or > (strict inequality) a dashed line (We exclude the line.) Step 2: Decide which half-plane to shade. • Pick a test point not on the boundary line. 0,0 ( ) is usually the best choice if it doesn't lie on the line. • If the coordinates of the test point make the inequality true, shade the half-plane containing the test point (i.e., shade “towards” the test point). Otherwise, shade the other half-plane (i.e., shade “away from” the test point).
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(Sections 7.5-7.6: Graphing Inequalities and Linear Programming) 7.37 Method 2: "Solve for y " Method Step 1: Put the inequality in the form
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M1410705 - (Sections 7.5-7.6: Graphing Inequalities and...

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