The line tangent to a function at (assuming the derivative exists at this point) is found by the point slope formula:
Writing this in slope-intercept form, we have:
Now, using and can you now compute the required -intercept?
Your derivative is correct, and next you correctly cite the point-slope formula for a line, but after that you contradict yourself/make wrong statements, and I am not sure what you really mean. I think what I stated is about as simple as it gets.