Question

Penny bought a juice squeezer for $10. She can make a bottle of orange juice for a cost of $0.75, and she sells her orange juice for $1.85 per bottle.
Which of the following graphs best illustrates Penny’s situation?
I.A graph has bottles on the x-axis and cost (dollars) on the y-axis. The cost line goes through (0, 10) and (3, 12.5) and the revenue line goes through (0, 0) and (4, 7.5). The cost and revenue lines intersect around (9, 17.5).
II.A graph has bottles on the x-axis and cost (dollars) on the y-axis. The cost line goes through (0, 10) and (3, 12.5) and the revenue line goes through (0, 10) and (4, 17.5). The cost and revenue lines intersect around (0, 10).
III.A graph has bottles on the x-axis and cost (dollars) on the y-axis. The cost line goes through (0, 10) and (13, 9) and the revenue line goes through (0, 0) and (4, 7.5). The cost and revenue lines intersect around (5, 9.5).
IV.A graph has bottles on the x-axis and cost (dollars) on the y-axis. The cost line goes through (0, 10) and (8, 25) and the revenue line goes through (0, 0) and (10, 7.5).


a.
I
b.
II
c.
III
d.
IV

Answer 1

Answer: I

Reason: Cost C(x) = 10 + 0.75x (y‑intercept 10, slope 0.75) and revenue R(x) = 1.85x (through origin, slope 1.85). Graph I shows a cost line starting at 10 and a revenue line through the origin with the revenue slope steeper than the cost; the other graphs have wrong intercepts or wrong slopes (II has revenue starting at 10, III has a decreasing cost, IV swaps the slopes).