SOLUTION: a. Sheena sells gourmet pastries on the Internet. In the fourth month of operation, she sold 480 dozen pastries, and in the seventh month she sold 792 dozen. Assume that we can m

Question 557222: a. Sheena sells gourmet pastries on the Internet. In the fourth month of operation, she sold 480 dozen pastries, and in the seventh month she sold 792 dozen. Assume that we can model the increase in her business by a linear equation. Find the equation of the line that models Sheena�s number of dozens in terms of the month. Write your answer in the form d = mt + b, where d is the number of dozens and t is the number of the month. Write an equation using two points from the problem.
I have began to solve this problem by finding the slope of the two given points. After I find the slope I am a little confused as to how I am suppose to write my answer in the form of d= mt + b
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
d = mt + b
d = dozens of pastries
m = slope
t = time
b = d intercept = value of d when t = 0
you find the slope by taking the difference in the dozens of pastries and dividing it by the months between those values.
you started with 480 dozen pastries in the 4th month.
you ended with 792 dozen pastries in the 7th month.
your slope is equal to (792-480) / (7-4) which becomes:
m = 312 / 3 which results in:
m = 104
your equation becomes:
d = 104*t + b
you now want to find the d intercept.
that's the value of d when t = 0
you find this by taking one of the points you used to form your equation.
take 792 dozen pastries in the 7th month.
replace d with 792 and raplace t with 7 to make this equation:
792 = 104*7 + b
now you want to solve for b.
you will wind up with:
b = 64
your equation becomes:
d = 104*t + 64
when t = 0, d = 64
when t = 4, d = 104*4 + 64 = 480
when t = 7, d = 104*7 + 64 = 792
you can graph this equation if you raplace d with y and you replace t with x.
your equation becomes:
y = 104*x + 64
here's the graph:

i placed horizontal lines at y = 480 and y = 792 so you can see the value of x when y equals those values. just trace down vertically from the intersections of those lines with the line of the equation.

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