A career-placement test eliminates a profession when a person receives a score of 18 or less. The score is equal to the formula 2x - 3y, where x is the number of positive responses and y is the number of negative responses. Which graph represents the range of test results that would be eliminated under this scenario (all points may not apply to the scenario)?

Graph is attached as an image

Step-by-step explanation:

A profession is rejected if the test scores of the person is 18 or less than 18.

So, the profession will be rejected when:

Test Scores ≤ 18

The formula to calculate the test scores is:

Difference of twice of number of items with positive response and thrice of number of items of negative response.

Let "x" represents the items with positive response and "y" represents the items with negative response. So the formula to calculate the test scores will be:

Test scores = 2x - 3y

Combining the two equations mentioned above, we get:

2x - 3y ≤ 18

A profession will be eliminated when the above inequality is satisfied. We have to find, which graph represent this situation where a profession will be eliminated based on the test scores.

The corresponding equation for the inequality is:

2x- 3y = 18

For x = 0. we get y = -6

For y = 0, we get x = 9

So, the two points on the graph will be (0, -6) and (9, 0). Plotting these points on graph and joining them with a straight line we get the graph of the equation.

Since, the inequality has equal sign as well, the graph of the line will be full(solid) line not dashed line. In order to check which region will be included in the solution, we test a point (0, 0) by substituting it in the inequality.

2(0)-3(0) ≤ 18

0 ≤ 18 , which is true.

So, the region which includes the point (0, 0) will be shared and will be the solution of the inequality, as shown in the graph below.

The shaded region represents the combination of responses that are possible for a profession to be eliminated.