Question 557222
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:
{{{graph(600,600,-1,10,-100,1000,104*x+64,480,792)}}}
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.