Suppose f(x)=Ax+B for real constants A and B. If f(60)=70 and f(72)=79, find k such that f(k)=k.

PLEASE HELP :]

Ok we have f(x)=Ax+B which is a line.
We also know
(1) f(60)=70 which means A*60+B=70
(2) f(72)=79 " " A*72+B=79
Which means A*12=9 if we subtract (1) from (2). Thus A=3/4 and B=25
Now we want (3/4)k+25=k or (1/4)k=25
You can finish and verify it.

To find the value of k where f(k) = k, we substitute the values of A and B into the equation for f(x).

We have f(x) = (3/4)x + 25.

Now, we set f(k) equal to k:

(3/4)k + 25 = k

To solve for k, we need to get rid of the fractions. Multiply both sides of the equation by 4 to clear the fractions:

3k + 100 = 4k

Next, subtract 3k from both sides of the equation:

100 = k

Therefore, the value of k that satisfies f(k) = k is k = 100.