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

Answer 1

Let x = number of 6‑passenger cars and y = number of 3‑passenger cars. The requirement is

6x + 3y ≥ 12 → divide by 3 → 2x + y ≥ 4 → y ≥ 4 − 2x.

The boundary line is y = 4 − 2x, which goes through (0, 4) and (2, 0), and because of ≥ the line is solid and the region above it is shaded. That corresponds to the graph that shows the line through (0,4) and (2,0) with everything to the left of the line shaded.