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.)
Answer
A
Image with description 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.
B
Image with description 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.
C
Image with description 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.
D
Image with description 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.
Explanation
If x is the number of 6-passenger cars and y is the number of 3-passenger cars, the passenger total is 6x + 3y. At least 12 passengers means 6x + 3y ≥ 12, or 2x + y ≥ 4. The boundary line has intercepts (0, 4) and (2, 0), and the solutions lie above and to the right of it, as shown in choice A.
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