Question

Find the equation of the tangent line to
y = ln x
at
x = 1.

Answer 1

Writing the equation of a straight line requires that you first have the slope and one point on the line. The point-slope form of the equation of a straight line is\[y-y _{1}=m(x-x _{1})\]
Substitue your values for m, x_1 and y_1 into this equation, and then simplify the equation. Done. Please show your work.

Answer 2

Note: In this problem, the slope of the tangent line is the derivative of y=ln x, evaluated at x=1. Thus, x_1 is = to 1. Using the formula y=ln x, calculate the value of y_1.