Answer:
The graph of the inequality 2x + 3y > 9 is the line 2x + 3y = 9 with the half-plane above it shaded.
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Explanation:
To graph the linear inequality 2x + 3y > 9, we need to first graph the boundary line 2x + 3y = 9, which is a straight line. To do this, we can solve for y and get:3y = -2x + 9y = (-2/3)x + 3
Now, we can graph this line by finding two points on the line. We can use the x-intercept and the y-intercept:
When x = 0, y = 3. So the y-intercept is (0, 3).
When y = 0, 2x = 9, so x = 4.5. So the x-intercept is (4.5, 0).
The line passes through (0, 3) and (4.5, 0).
Now, to graph the inequality, we need to determine which side of the line satisfies the inequality. We can do this by picking a test point that is not on the line, such as (0, 0), and plugging it into the inequality:
2x + 3y > 92(0) + 3(0) > 90 > 9
Since 0 is not greater than 9, (0, 0) is not a solution to the inequality. Therefore, the half-plane that does not contain (0, 0) satisfies the inequality.