Question 80886
I would start with the slope-intercept form of a linear equation:
y = mx + b
But, because you are addressing variables that are different from x (the independent variable) and y (the dependent variable), I would change to the variables P (the independent variable) and C (the dependent variable).

In this problem, C (the number of cups sold) is the dependent variable because it depends on the price (P) that is charged for each cup.
Since you are given two ponts (P, C) on the line: (2, 120) and (3, 60) you can find the slope, m by using the slope formula: {{{m = (y[2]-y[1])/(x[2]-x[1])}}} or, in your variables:{{{m = (C[2]-C[1])/(P[2]-P[1])}}}
{{{m = (60-120)/(3-2)}}}
{{{m = -60/1}}}
{{{m = -60}}}
So you can write:
C = -60P + b  Remember, we are substituting C for y and P for x.
Now you need to find the value of b, the y-...oops, I mean the C-intercept.
You can do this by substituting the C and P values from one of the given points, say (3, 60) into this equation and solve for b.
60 = -60(3) + b Simplify.
60 = -180 + b Add 180 to both sides.
240 = b

Now you can write the final equation:

C = -60P + 240

Check:
For P = $2 and C = 120 cups:
120 = -60(2)+240
120 = -120+240
120 = 120

...and for P = $3 and C = 60 cups:
60 = -60(3)+240
60 = -180+240
60 = 60