# Thread: tangent line problems

1. ## tangent line problems

a) Find an equation on the tangent line to the graph of y=g(x) at x= 5 if g(5) = -3 and g'(5) = 4

b) If the tangent line to y = f(x) at (4,3) passes through the point (0,2), find f(4) and f'(4)

2. ## re: tangent line problems

Use the point slope formula...

$y - y_1 = m(x - x_1)$

The point $(x_1 , y_1) = (5, -3)$

The slope is 4.

3. ## re: tangent line problems

Originally Posted by angelamonique
a) Find an equation on the tangent line to the graph of y=g(x) at x= 5 if g(5) = -3 and g'(5) = 4

b) If the tangent line to y = f(x) at (4,3) passes through the point (0,2), find f(4) and f'(4)
The tangent line at $(x_0,g(x_0))$ is $y-g(x_0)=g'(x_0)(x-x_0)~.$

4. ## re: tangent line problems

Thank you, but can you also tell me how you figured that out?

5. ## Re: tangent line problems

They attended class! One of the basic definitions of the derivative is that it is the slope of the tangent line.

6. ## Re: tangent line problems

Originally Posted by HallsofIvy
They attended class! One of the basic definitions of the derivative is that it is the slope of the tangent line.
I wasn't sure exactly how to approach that!

Indeed, the veracity/validity/whatever of the point slope formula should not be called into question at this juncture. So we're left with the task of finding a point and a slope, in order to determine the desired line.
Welp, g(5)=-3 means that (5, -3) is the point.
And you really DO need to know that the slope of the tangent is given by the derivative.