Question

A shipping box can carry no more than 6 pounds. Each order of jumbo paperclips weighs 2 pounds, and each order of packing tape weighs 3 pounds. If x is the number of paperclip orders and y is the number of packing tape orders, which graph models the combinations that can be shipped together?

On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (3, 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 (3, 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, 3) and (2, 0). Everything to the right of the line is shaded.

On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the left of the line is shaded.

Answer 1

Write the weight constraint: 2x + 3y ≤ 6.
The intercepts are (0,2) and (3,0), the boundary line is solid, and the feasible region is the set of points below/left of the line.

So the first graph is correct.