Question

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)?

Answer 1

Eliminated when 2x − 3y ≤ 18. Rearranging gives

2x − 3y ≤ 18 ⇒ −3y ≤ 18 − 2x ⇒ 3y ≥ 2x − 18 ⇒ y ≥ (2/3)x − 6.

So the correct graph shades the region on or above the line y = (2/3)x − 6 (including the line), with x ≥ 0 and y ≥ 0 since x and y are counts.