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, tape is 3 lbs, total ≤6 lbs:
$2x + 3y \leq 6$

Step2: Find x-intercept (y=0)

Set $y=0$, solve for $x$:
$2x = 6 \implies x=3$

Step3: Find y-intercept (x=0)

Set $x=0$, solve for $y$:
$3y = 6 \implies y=2$

Step4: Determine valid region

Since $x,y$ are non-negative (orders can't be negative), and we need values where total weight is ≤6 lbs, the region is below the line, in the first quadrant.

Answer:

The correct graph is the second one (top middle), with intercepts at (3, 0) and (0, 2), and the shaded region below the line in the first quadrant.