Question 662256
 = number of quarts
 = price in $

(Explanation: We have to start by defining variables that will be related by a linear equation. Next, we have to use the two (x,y) data points given to find the equation)

one gallon (4 quarts) for $3.09 --> (4,3.09) (x=4, y=3.09)
half gallon (2 quarts) for $1.65 --> (2,1.65) (x=2, y=1.65)

a) Write the particular equation expressing price in terms of quarts.
(Explanation: We are looking for an equation of the form . We can substitute the (x,y) values for each data point to get a system of equation to solve for  and . Otherwise, we can use the two points to calculate the slope  of the line, and then we can find the rest of the equation one way or another) 
Using a system of equations:

Subtracting the second equation from the first equation;

-
-----------------
 -->  --> 
Substituting that value in the second equation, we get
 -->  -->  --> 
The equation is  
Using slope:
(Explanation: the slope,  in the change in y divided by the change in x, as we go from one data point to the other.)
 -->  --> 
The point-slope form of the equation, using point (2,1.65), is:

 -->  -->  --> 

b) If Handy Andy sold 3-gallon cartons, what would your equation predict the price to be?

Substituting  in the equation, we get
 -->  --> 
Andy would sell a 3-gallon carton for $8.85. 

c) The actual prices for pint cartons (1/2 quart) and one-quart cartons are $.57 and $.99, respectively. Do these prices fit your mathematical model? If not, are they higher than predicted or lower?
The predictions are found using the equation 
For 1/2 quart =  quart, , so
 -->  --> 
For 1 quart, , so
 -->  --> 
the price for pint cartons agrees with the  prediction,
but the price for the quart, $0.99, is higher than the  prediction.

d)
I would use  and the equation  to find the number of quarts, .

 a carton would hold 4.5 quarts according to the model.

e)
The price-intercept is the y-intercept in the equation .
It is the value, , representing $0.21, the price of a carton with zero quarts of milk inside. It represents the cost of the carton plus maybe Andy's work making a sale.

f) What are the units of the slope? What real-world quantity does this number represent?
The slope, , represents the cost of the milk per quart.
The units are $/quart, and it gets multiplied by the number of quarts to find the price of the milk inside the carton in $.