Problem

For \(C=4x+12\); \(\text{point}(5,32)\); \(x\) is items and \(C\) is dollars, identify input quantity/unit, output quantity/unit, equation check, and contextual point interpretation.

A fully scaled graph of C equals 4x plus 12 with items on the horizontal axis, cost in dollars on the vertical axis, and dashed guides locating the given point (5, 32).

Big Picture

What this problem is really about

A point on this graph is an input-output pair, so the first coordinate uses item units and the second uses dollar units. We’ll substitute the input into the full cost equation to verify the output, then describe the pair as one total-cost situation without mistaking the ratio of its coordinates for the per-item rate.

Answer choices

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Preview only

input coordinate=5 items; output coordinate=32 dollars; substitution=C(5)=4·5+12=32; interpretation=total cost for5 items is32 dollars

input coordinate=5 items; output coordinate=20 dollars; substitution=C(5)=4·5=20; interpretation=total cost for5 items is20 dollars

input coordinate=5 items; output coordinate=32 dollars; substitution=32÷5=6.4 dollars/item; interpretation=the model's unit rate is6.4 dollars per item

input coordinate=32 dollars; output coordinate=5 items; substitution=C(32)=4·32+12=140; interpretation=32 items have a total cost of5 dollars

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For \(C=4x+12\); \(\text{point}(5,32)\); \(x\) is items and \(C\) is dollars, identify input quantity/unit, output quantity/unit, equation check, and contextual point interpretation.

What this problem is really about

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