Explanation Procedure used: “To graph a linear inequality in two variables: 1. Find the boundary by graphing an equation that substitutes an equal sign for the inequality symbol. Make a solid line if the boundary is included ( < or > ) or a dashed line if the boundary is not included ( < or > ) in the solution set. 2. Test any point that is not on the boundary line. 3. If the test point makes a true statement with the original inequality, shade the side containing the test point. 4. If the test point makes a false statement with the original inequality, shade the side opposite the side containing the test point.” Calculation: From the given, the inequality is observed to be a strict inequality. So, the boundary will not be included in the solution set. Thus, the dashed line is used to represents the line. Replace the given inequality with equal sign. y = − 3 2 x + 1 2 Compare the equation y = − 3 2 x + 1 2 with y = m x + b and obtain the value of m and b . y = m ↓ x + b ↓ y = − 3 2 x + 1 2 The coefficient of x is observed to be − 3 2 . Thus, the slope of the equation is − 3 2 or 3 − 2 . Similarly, the value of b is 1 2 , so the y -coordinate of y -intercept is 1 2 . Thus, the y -intercept is ( 0 , 1 2 ) . Now obtain the additional points as follows. Since the slope is − 3 2 , vertically move 2 unit right in the x -axis and move horizontally 3 units downward in y -axis from the y -intercept ( 0 , − 3 ) . That is, add 2 unit and subtract 3 unit to the x -coordinate and y -coordinate of ( 0 , 1 2 ) , respectively. Thus, the first point on the line is ( 2 , − 5 2 ) . Similarly other slope is 3 − 2 , move 2 unit left from the point ( 0 , 1 2 ) in the x -axis and move 3 units upward in y -axis

MML F/COLLEGE MAT F/TRADES - ACCESS CODE

10th Edition

ISBN: 9781323845967

Author: Hobbs

Publisher: PEARSON

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Chapter 9.2, Problem 50E

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To sketch: The graph of the inequality y>−32x+12 using test points.

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Chapter 9.2, Problem 49E

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MML F/COLLEGE MAT F/TRADES - ACCESS CODE

Ch. 9.1 - Find y if x = 4 in the equation 3x + 2y = 6. Ch. 9.1 - Locate the points in Fig. 9–12 by giving the...Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - Prob. 9E

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The graph of the inequality y &gt; − 3 2 x + 1 2 using test points.

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The graph of the inequality y > − 3 2 x + 1 2 using test points.