# Thread: Find the equation of tangent line

1. ## Find the equation of tangent line

Hello,
I need to find the tangent line to the grapg of y=g(x) at x=5 if g(5) = -3 and g'(5) = 4

Can anybody give me a hint how I can do that?
Thanks

2. Originally Posted by DBA
Hello,
I need to find the tangent line to the grapg of y=g(x) at x=5 if g(5) = -3 and g'(5) = 4
The tangent line to the graph of $y=g(x) \text{ at } x_0$ is $y-g(x_0)=g'(x_0)(x-x_0)$.

3. So,
y-g(5)=g'(5)(x-5)
y+3=4(x-5)
y+3=4x-20
y=4x-23

Is that correct?

4. that is correct.

The equation for a line can be written like $y=kx+c$

$g'(5)=4$ gives you the slope of the line (k)

and $g(5)=-3$ gives you a point in the tangent line (x and y)

Knowing that,

$-3=4*5+c$
$-3=20+c$
$c=-23$

$y=4x-23$