Derive directly to get y'=4x, and substitute x=- 1 to get y'=-4, so the slope is -4.
Example 2. The tangent equation of curve y = x 3+1 at (1,2) is _ _ _ _ _ _ _ _ _ _ _?
Take the derivative first, y'=3x 2, and substitute x= 1 to get y' = 3.
Let the tangent equation be y=3x+b, and 3 is the slope just obtained, because the point (1, 2) passes through both the original straight line and the tangent line, and b=- 1 is obtained by substitution.
So the tangent equation is y=3x- 1.