Question

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)?

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.

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.

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.

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.

Answer 1

Let x = sofas and y = pairs of pillows. Total items = x + 2y, and the wholesaler requires at least 4 items, so

x + 2y ≥ 4.

The boundary line x + 2y = 4 goes through (0,2) and (4,0) and is solid because equality is allowed. Test (0,0): 0 + 2·0 < 4, so the region is the opposite side (above and to the right) of the line.

So the correct graph is the fourth option: a solid line through (0,2) and (4,0) with the region above/right of the line shaded.