Basically, you have two points on a line (p(1),n(1)) and (p(2),n(2)), and you use these in the linear equation y=mx+b, or in your case, n(p)=mp+b. First, you must notice that the question asks for n in terms of p, take out the middle words, and you have n of p, or written mathematically n(p). This is why I have set up p as the first coordinate in the ordered pair, it is independent, n depends on it. Now, you can either use point-slope form

y-y(1)=m(x-x(1)) (or for this p-p(1)=m(n-n(1)))

or you can use slope-intercept

y=mx+b

(which for some reason is easier to remember but mathematically it takes longer to solve). First, you must find the slope:

m=(p(2)-p(1))/(n(2)-n(1))=(25-50)/(12-8)

Then solve the equation

p-50=(-25/4)(n-8) or

p-25=(-25/4)(n-12)

for p (either one you use, you will come up with the same answer). Or you can solve

50=(-25/4)(8)+b

for b and plug it back into n(p)=mp+b, and again you should get the same answer which is:

n(p)=(-25/4)p+100.

Try solving both ways, just for practice. To check your answer, plug either point back in and make sure you have equality. That's the great thing about math, you know when you're right!!

Have Fun,

jsmath22