Solve $3x + 2y > 6$ graphically.
(N/A) The graph of $3x + 2y = 6$ is represented by a dotted line in the figure.
This line divides the $xy$-plane into two half-planes,$I$ and $II$. We select a test point not on the line,such as $(0, 0)$,which lies in half-plane $I$,and determine if it satisfies the given inequality:
$3(0) + 2(0) > 6$
$0 > 6$,which is false.
Hence,half-plane $I$ is not the solution region. Since the inequality is strict $(>)$,points on the line are not included. Therefore,the shaded half-plane $II$ represents the solution region of the inequality.
This line divides the $xy$-plane into two half-planes,$I$ and $II$. We select a test point not on the line,such as $(0, 0)$,which lies in half-plane $I$,and determine if it satisfies the given inequality:
$3(0) + 2(0) > 6$
$0 > 6$,which is false.
Hence,half-plane $I$ is not the solution region. Since the inequality is strict $(>)$,points on the line are not included. Therefore,the shaded half-plane $II$ represents the solution region of the inequality.
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