Question 1151880
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Temporarily, I'm going to use x instead of P. 
Also, I'll use y in place of n. 
At the end I'll do replacements.


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x = price
y = number of DVDs


"One month a store sells dvds for $5 Each and sells 1200 DVDs." means we have the point (x1,y1) = (5, 1200)


"The next month they charge $7.50 and sell 800 dvds" means we have the point (x2,y2) = (7.5, 800)


Calculate the slope
{{{m = (y[2] - y[1])/(x[2] - x[1])}}}


{{{m = (800 - 1200)/(7.5 - 5)}}}


{{{m = (-400)/(2.5)}}}


{{{m = -160}}}
The slope tells us that for each price increase of $1, the number of DVDs sold goes down by 160.


Now turn to the point-slope formula. Plug in the given info. Solve for y.
{{{y-y[1] = m(x - x[1])}}}


{{{y-1200 = -160(x - 5)}}}


{{{y-1200 = -160(x) - 160(-5)}}}


{{{y-1200 = -160x + 800}}}


{{{y = -160x + 800+1200}}}


{{{y = -160x+2000}}}


{{{n = -160*P+2000}}} Replace x with P, replace y with n.



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Check: 


We should plug in a price of P = 5 and get n = 1200
{{{n = -160*P+2000}}}
{{{n = -160*5+2000}}}
{{{n = -800+2000}}}
{{{n = 1200}}}
so that works out. Also, plugging in P = 7.5 should lead to n = 800
{{{n = -160*P+2000}}}
{{{n = -160*7.5+2000}}}
{{{n = -1200+2000}}}
{{{n = 800}}}
that works as well. We have the proper equation.


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Answer: {{{n = -160*P+2000}}}
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