Question 202710
Ok, let's use the "slope-intercept" form (y = mx+b) of a linear equation to develope the necessary equation, except that our "dependent variable" will be C (for number of cups) rather than y and our "independent variable" will be P (for price) rather than x.
So we can start with:
{{{C = highlight_green(m)*P+highlight(b)}}} where m is the slope of the line and b is the y-intercept.
The problem gives us two points to start us off.
P = $2 & C = 120 cups. We can write this as an ordered pair (2, 120)
P = $3 & C = 60 cups.  We can write as an ordered pair (3, 60)
Now we have two points that will satisfy our equation, we can calculate the slope, m, from the formula for the slope.
{{{m = (y[2]-y[1])/(x[2]-x[1])}}} but, instead of using x and y, we want to use P and C respectively, so...
{{{m = (C[2]-C[1])/(P[2]-P[1])}}} Substitute: {{{C[1] = 120}}}, {{{C[2] = 60}}}, {{{P[1] = 2}}}, and {{{P[2] = 3}}}
{{{m = (60-120)/(3-2)}}} Evaluate.
{{{m = (-60)/1}}}
{{{highlight_green(m = -60)}}} So now we have...
{{{C = -60P+b}}} Next, we need to find the value of b, the y-intercept (or, in this problem, the C-intercept).  This is done by substituting the C- and P-values from either one of the two given points that we started off with.
Let' use (2, 120).
{{{120 = -60(2)+b}}} 
{{{120 = -120+b}}} Add 120 to both sides.
{{{240 = b}}} or {{{highlight(b = 240)}}} 
Ok, we can now write the final equation:
{{{highlight(C = -60P+240)}}}