Thread: Finding equation of a tangent line given slope of tangent

This question should be easy but it's giving me some trouble. I am asked to find the equation of the tangent to and told that the slope of the tangent is 1.

It is worded exactly: "Find the equation of a the tangent line to the graph that has slope 1.

So I found the derivative of f(x) to be

I then substituted f'(x) with 1 and found that x=1/2.

I substituted 1/2 into the original equation for x and found that f(x)= 1/8.

I then used (y-1/8)=1(x-1/2) and found the equation of the tangent to be y=x-3/8

The answer in my book was 8x-8y-3=0

Where did I go wrong?

Originally Posted by Apathy

This question should be easy but it's giving me some trouble. I am asked to find the equation of the tangent to and told that the slope of the tangent is 1.

It is worded exactly: "Find the equation of a the tangent line to the graph that has slope 1.

So I found the derivative of f(x) to be

I then substituted f'(x) with 1 and found that x=1/2.

I substituted 1/2 into the original equation for x and found that f(x)= 1/8.

I then used (y-1/8)=1(x-1/2) and found the equation of the tangent to be y=x-3/8

The answer in my book was 8x-8y-3=0

Where did I go wrong?

Multiply the last equation by 8.

You have the same answer as the textbook. Just multiply through by 8.

You need where is the solution to

Why don't I use the y-coordinate?

See reply #3

I finally understand. Thanks everybody!