Question

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

Answer 1

Question (a), (b) and (c):

Solution:

a) According to the graphs, we can conclude that

1) The left-hand graph is the cost in dollars vs drink volume in ounces.

2) The right-hand graph is the calories vs drink volume in ounces.

b) If you take the points (x,y) of the right-hand graph, and you perform a ratio between them obtains a proportionality. In fact, this proportionality is the constant of proportionality:

`(y)/(x)\text{ =}(150)/(10)\text{ =}(360)/(24)=\text{ 15}`

thus, the quantities (coordinates of the points) that appear in the right-hand graph are in a proportional relationship.

c) The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate. The constant of proportionality k is given by

`k=(y)/(x)\text{ =}(150)/(10)\text{ =}(360)/(24)=\text{ 15}`