Answer:
[tex]y=\frac{f(A)-f(0)}{A}x+f(0)[/tex]
Step-by-step explanation:
Ok we have two intersections:
One point of intersection is (0,f(0)).
Another point of intersection is (A,f(A)).
Slope-intercept form of a linear equation is y=mx+b where m is the slope and b is the y-intercept.
We actually are given the y-intercept is f(0). That means b=f(0).
Now we need to calculate the slope which is rise/run or change in y over change in x.
I'm going to find the slope by lining up the points vertically and subtracting vertically, then will put 2nd difference over 1st difference.
Like so:
(A. , f(A))
-(0. , f(0))
--------------
A f(A)-f(0)
So the slope is [tex]\frac{f(A)-f(0)}{A}[/tex].
We are now ready to give our answer for the linear equation in slope-intercept form.
We have [tex]m=\frac{f(A)-f(0)}{A}[/tex] and [tex]b=f(0)[/tex].
Entering into y=mx+b form:
[tex]y=\frac{f(A)-f(0)}{A}x+f(0)[/tex]
