Question

(05.05) Which inequality matches the graph? (2 points)​

Answer 1

Answer: Choice C  $-3x+2y \ge 7$

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Explanation:

The boundary line is solid, so that means we'll be dealing with "or equal to" as part of the inequality sign. The answer is between choice A and choice C because of this.

Note how the point (0,0) is not in the shaded region. This must mean that plugging x = 0 and y = 0 into the answer will lead to a false statement.

If we plug x = 0 and y = 0 into choice A, then we get...

$3x-2y \le 7\\\\3(0)-2(0) \le 7\\\\0 \le 7$

Which is a true statement, implying that (0,0) is in the shaded region. However, we're after a false statement, so we can rule out choice A.

The answer must be choice C

Let's plug (x,y) = (0,0) into choice C

$-3x + 2y \ge 7\\\\-3(0) + 2(0) \ge 7\\\\0 \ge 7$

That is false because 0 is not equal to 7, nor is it larger than 7.

This helps confirm that choice C is the answer.