If the tangent line to y = f (x) at (9,7) passes through the point (0,6)

[Pondera]

Homework Statement

If the tangent line to y = f (x) at (9,7) passes through the point (0,6), find the following.

(a) f (9)

(b) f ' (9)

Homework Equations

f '(x) = f(x+h) - f(x)/h ?

The Attempt at a Solution

I really have no idea how to even begin going about this one, so a shove in the right direction would be greatly appreciated.

 

[tony873004]

my guess:
Since the line is tangent to f(x) at (9,7), then (9,7) must be a point on f(x). If (9,7) is on the function, then when x=9, what is y? That's f(9).

You have 2 points on the tangent line. (9,7) and (0,6). Find the slope of this line using the slope formula: rise / run. Then remember that f'(9) is simply asking what's the slope of the function at (9,7), which is the same as asking what is the slope of the tangent line.

 

[Pondera]

Thank you very much! I'm not sure why I had such a hard time conceptualizing what that question was asking, but your hints were correct and I got it.