Question

A ride at an amusement park has two options for cars, one that holds 6 passengers and one that holds 3 passengers. If the ride designer wants to make sure that each run holds at least 12 passengers, which graph represents the overall equation and shows the possible combinations of the number of 6-passenger cars, x, and the number of 3-passenger cars y (not all points may apply to the scenario)?

On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything to the left of the line is shaded.

On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything above and to the right of the line is shaded.

On a coordinate plane, a solid straight line has a negative slope and goes through (0, 4) and (2, 0). Everything to the left of the line is shaded.

Answer 1

Total passengers: 6x + 3y ≥ 12. Divide by 3: 2x + y ≥ 4, so
y ≥ 4 − 2x.

The boundary line is y = 4 − 2x, which goes through (0, 4) and (2, 0) and is solid (≥). The feasible region is the half-plane above that line (which is the same side as the y-axis above (0,4)). Therefore the graph described in the third option (line through (0,4) and (2,0) with the appropriate side shaded) is the correct one.