Question

Write the equation in slope intercept form

Answer 1

Answer:

$y=\frac{f(A)-f(0)}{A}x+f(0)$

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 $\frac{f(A)-f(0)}{A}$.

We are now ready to give our answer for the linear equation in slope-intercept form.

We have $m=\frac{f(A)-f(0)}{A}$ and $b=f(0)$.

Entering into y=mx+b form:

$y=\frac{f(A)-f(0)}{A}x+f(0)$