8
QuizMultiple Choice

Modeling with Two-Variable Linear Inequalities — Quiz

Question 8 • Mathematics I

A hook in an office storage closet can hold no more than 6 pounds. An order of jumbo paperclips weighs 2 pounds and an order of packing tape weighs 3 pounds. If x is the number of orders of paperclips and y is the number of orders of packing tape, 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 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.
B
Image with description 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.
C
Image with description 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.
D
Image with description 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.

Explanation

The total weight is 2x + 3y pounds, and it can be no more than 6, so the inequality is 2x + 3y ≤ 6. Its boundary line crosses the x-axis at (3, 0) and the y-axis at (0, 2). Because the hook can hold exactly 6 pounds, the line is solid, and the allowed region is below and to the left of it. This matches the graph in choice A.

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