Question

a company will make $150000 profit if it manufactures 1000000 items and $1750000 profit if it manufactures 500000 items. the relationship bewteen the number of drives manuactured and the profit is a linear. write an equation that gives the profit P when n items are manufactured

Answer 1

This is an inverse function, so it will look a little funky. Don't get confused with the slope and y intercept:

We can say our intervals will be [1,5] in millions.
Since initial profit will = $150,000 and x = 0, we can use this as the y-intercept.

Now, to find the rate at which profit is changing, you can either think of it intuitively (from x =1 to x=5), you can go ahead and get out a scratch piece of paper. Using our favorite formula, the rate of change of profit generated from 1 to 5 is:

f(b)-f(a) / b-a. So, we're given our y values, giving us this guy: 175000-150000/5 mil - 4 mil, which = 1.6 (in millions).
The line is y=1.6x+150,000