(a) Find the slope of the tangent line to the curve y = 9-x^{2} at the point whose x-coordinate is 2.
(b) Find the equation of this tangent line in a slope-intercept form.
(a) $\displaystyle \frac{dy}{dx} = -2x$. Particularly, at x = 2, $\displaystyle \frac{dy}{dx} = -2(2) = -4$. Slope is -4.
(b) We know that the function goes through the point (2,5) (substituted x=2 into the original function). Therefore we can write in point-slope form and convert to slope-intercept form:
$\displaystyle y-5 = -4(x-2) \Rightarrow y = -4x + 13$