Finding the equation of the tangent line

[Mathamateur]

Alright, I've got half of this problem done and I don't know where to go from here.


Find the slope of the tangent line to the given curve at the given value of x. Find the equation of each tangent line

y = ln x; x = 1

I found the derivative dy/dx = 1/x
and therefore found the slope = 1

Am I right so far?
Now how do I find the equation of the tangent line?

 

[wjm11]

Find the slope of the tangent line to the given curve at the given value of x. Find the equation of each tangent line

y = ln x; x = 1

I found the derivative dy/dx = 1/x
and therefore found the slope = 1

Go back to the original function, y = lnx, plug in 1 for x and find the corresponding y value. Now you have a point: (1, ln(1)), (which happens to be (1,0)). You now have the slope of the line and a point on the line, so you can write the equation of the line.

 

[Mathamateur]

Find the slope of the tangent line to the given curve at the given value of x. Find the equation of each tangent line

y = ln x; x = 1

I found the derivative dy/dx = 1/x
and therefore found the slope = 1

Go back to the original function, y = lnx, plug in 1 for x and find the corresponding y value. Now you have a point: (1, ln(1)), (which happens to be (1,0)). You now have the slope of the line and a point on the line, so you can write the equation of the line.

So the equation would be
y = x -1

Correct?

 

[tkhunny]

Why do you doubt? Good work.