Answer
$y=\frac{1}{2}x-\frac{1}{2}$
Work Step by Step
In order to find the equation of a tangent line, first you need to take the derivative. For this equation, just use the Power Rule.
$y=x−\sqrt x$
$y=x−x^{1/2}$
$Power Rule: \frac{dy}{dx}=nx^{n−1}$
$dy/dx=1-\frac{1}{2}x^{-1/2}$
The derivative is your equation of the slope. To find the slope at the point (1,0), plug in x=1 into the derivative equation:
$dy/dx \Bigr|_{\substack{x=1}}= 1-\frac{1}{2}(1)^{-1/2} = 1/2.$
Now to get the equation of the tangent line, use point-slope form:
$y−y1=m(x−x1)$
$y−(0)=(1/2)(x−(1))$
$y=\frac{1}{2}x-\frac{1}{2}$
