word problem - makes no sense!?
Suppose that a market research company finds that at a price of p = $40, they would sell x = 37 tiles each month. If they lower the price to p = $25, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. (Hint: Write an equation using two points in the form (x,p)).
Comments
Oh, it makes plenty of sense. They are giving you two points on a line, (x, p) = (37, 40) and (52, 25) and they want you to write the equation of the line.
p - 40 = (25-40)(x-37)/(52-37)
p = 40 - (15/15)(x-37)
p = 40 - x + 37
The line in slope intercept form is:
p = -x + 77
where the slope = -1 and the intercept = 77.
...
It helps to think of p as a y.
In y=mx+b form m is the slope and b is the point at which the line crosses the y axis
Use the points (37,40) and (52,25) to determine the slope with (y1-y2)/(x1-x2) so (37-52)/(40-25)=-15/15 or -1 so y=-1x+b. Now we plug in one coordinate to find b: 40=-1(37)+b so 40=-37+b so 77=b therefore your equation is: y=-1x+77