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

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Answer 1 · 2016-10-06T02:57:08

#y = 4 x - 7#

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'(x) = 2x#

#y'(2) = 2(2) = 4#

#m = 4#

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

#1 = 4(2) + b#

#b = -7#

The equation of the tangent line is:

#y = 4 x - 7#