A wholesaler requires a minimum of 4 items in each order from its retail customers. The manager of one retail store is considering ordering a certain number of sofas, x , and a certain number of pillows that come in pairs, y Which graph represents the overall equation represented by this scenario? (All points may not apply to the scenario.)
Answer
A
Image with description On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.
B
Image with description On a coordinate plane, a dashed 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.
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 above and to the right 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 below and to the left of the line is shaded.
Explanation
Each sofa counts as 1 item, and each pair of pillows counts as 2 items, so the order contains x + 2y items. The minimum requirement is x + 2y ≥ 4, whose boundary line passes through (4, 0) and (0, 2). Since orders with exactly 4 items are allowed, the boundary is solid; orders with more items lie above and to the right of the line. This matches choice C.
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