The amount of caffeine consumed from a glass of Diet Pepsi is proportional to the number of ounces that was drank. The table below shows the amount of caffeine consumed by three different people and the corresponding number of ounces of Diet Pepsi that they each drank. Amount of Caffeine (mg) 27 45 72 Amount of Diet Pepsi (oz) 3 5 8 What is the unit rate (or constant of proportionality)? Write an equation to represent this proportional relationship. Make sure to define the variables you used.

Constant of proportionality: k=3

Equation: c=3d

Step-by-step explanation:

By definition, Direct proportion equations have the following form:

Where "k" is the Constant of proportionality.

In this case, let be "c"  the the amount of caffeine consumed  (in mg) from a glass of Diet Pepsi and "d" the number of ounces that was drank.

So, the equation that represents this relationship will have this form:

Then, the first step is to find the Constant of proportionality "k".

Knowing that:

We can substitute values into the equation:

Now, solving for "k", we get:

Therefore, we can write the following equation that represents that proportional relationship:

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.