how to construct a linear equation

a company knows that 280 units sell per month at a price of 195 per unit. for every 15 dollar hike in the price the number of units sold per month decreases by 10.

assume this relationship is linear and find an equation that expresses x in terms of p

for this question the text says the answer is x=410-(2/3)p

how do I know that that slope is -10/15 (or -2/3) as opposed to 15/-10?

also it seems that for this question x is treated as y and p is treated as x (the book uses change in x/ change in p to calculate the slope), is it normal for x to represent the vertical axis and for p to represent the horizontal axis? I thought that was only in econ.

Re: how to construct a linear equation

Quote:

Originally Posted by

**kingsolomonsgrave** a company knows that 280 units sell per month at a price of 195 per unit. for every 15 dollar hike in the price the number of units sold per month decreases by 10.

assume this relationship is linear and find an equation that expresses x in terms of p

Lets say x = mp+c, we need to find m = (280-270)/(195-210) = -10/15 = -2/3

Now x= -2/3p+c, to find c sub in some values i.e (195,280) gives 280 = (-2/3)*195+c

Solve for c and you are done!