Question

At a restaurant, hot chocolate can be purchased in two different cup sizes. A 12-ounce cup costs $4.80 and a 16-ounce cup costs $6.40.

Is the linear relationship between cup size and cost also proportional? Why or why not?

Yes, there is no constant of proportionality.
Yes, the constant of proportionality is 0.4.
No, the constant of proportionality is 0.4.
No, there is no constant of proportionality.

Answer 1

Answer:  Yes, the constant of proportionality is 0.4.

Work Shown

x = number of ounces

y = cost

k = constant of proportionality

k = y/x = 4.80/12 = 0.4

k = y/x = 6.40/16 = 0.4

We get the same result each time, so the constant of proportionality is 0.4

The direct proportion equation is y = 0.4x

Answer 2

Step-by-step explanation:

The linear relationship between cup size and cost is proportional. To verify this, we can calculate the constant of proportionality:

For the 12-ounce cup:

Cost = Constant of Proportionality × Cup Size

4.80 = Constant of Proportionality × 12

Constant of Proportionality = 4.80 / 12 = 0.4

For the 16-ounce cup:

Cost = Constant of Proportionality × Cup Size

6.40 = Constant of Proportionality × 16

Constant of Proportionality = 6.40 / 16 = 0.4

Since the constant of proportionality is the same for both cup sizes, the relationship between cup size and cost is indeed proportional, with a constant of proportionality equal to 0.4. Therefore, the correct answer is: "Yes, the constant of proportionality is 0.4."