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?

Explanation:

Step1: Define inequality for weight limit

Each paperclip order is 2 lbs, packing tape is 3 lbs. Total weight ≤ 6 lbs:
$$2x + 3y \leq 6$$

Step2: Find intercepts of boundary line

Set $x=0$: $3y=6 \implies y=2$. Set $y=0$: $2x=6 \implies x=3$. Boundary line connects $(0,2)$ and $(3,0)$.

Step3: Test origin for shaded region

Substitute $(0,0)$ into $2x+3y \leq6$: $0 \leq6$, which is true. Shade region containing the origin.

Step4: Verify non-negative values

$x,y$ are counts, so $x\geq0, y\geq0$. Valid region is in first quadrant, below the line.

Answer:

The correct graph is the middle one (with boundary line connecting (0,2) and (3,0), shaded region below the line including the origin and first quadrant values).