Question

The graphs below show some data from a coffee shop menu. One of the graphs shows cost (in dollar) vs. drink volume (in ounces), and one of the graphs shows calories vs. drink volume (in ounces.)

a. Which graph is which? Given them the correct titles.
Graph A: _______vs volume......... Graph B:_______vs volume

b. Which quantities appear to be in a proportional relationship?
1. cost vs volume or
2. calories vs volume
For the proportional relationship, find the constant of proportionality.
a. 0.21 per ounce,
b. 12 calories per ounce,
c. 0.38$ per ounce, or
d. 15 calories per ounce

Answer 1

a. Graph A: Cost vs Volume

Graph B: Calories vs Volume

b. Graph B (Calories vs Volume)

c. k = 15

Explanation:

a. It is not possible for a volume of 10 oz of drink to be sold for $150. It doesn't make common sense. Also, calorie level of 150 in 10 oz of drink seem plausible.

It makes more sense if 10 oz of the drink cost $3.75. Therefore, the graphs should be titled as follows:

Graph A: Cost vs Volume

Graph B: Calories vs Volume

b. The quantities in Graph B (Calories vs Volume) appear to be in a proportional relationship. We know this because if we try drawing a line to connect the points on the graph, it will give us a straight line. A straight line connotes proportionality.

Also the ratio of the quantities of the two known points given are the same. I.e.
`(150)/(10) = (360)/(24) = 15`

Therefore the quantities compared in Graph B shows a proportional relationship.

c. Constant of proportionality =
`(150)/(10) = (360)/(24) = 15`