# How do you find the equation of the tangent and normal line to the curve y=x^2-3 at (2,1)?

Oct 6, 2016

$y = 4 x - 7$

#### Explanation:

The slope, m, of the tangent line at any given point is the first derivative, y'(x), evaluated at the x coordinate of the given point.

$y ' \left(x\right) = 2 x$

$y ' \left(2\right) = 2 \left(2\right) = 4$

$m = 4$

Using the $y = m \left(x\right) + b$ form, we substitute, 1 for y, 2 for x, 4 for m, and then solve for b:

$1 = 4 \left(2\right) + b$

$b = - 7$

The equation of the tangent line is:

$y = 4 x - 7$