Line tangent to the curve, how to find gradient of line?

Question

The line is tangent to a curve at a point. How do i find the gradient of the line? The point of contact is (2,-5) and equation of the curve is y=x^2 - 3x -3.

Answer 1

gradient of tangent=dy/dx =d/dx(x^2-3x-3)
=2x-3
=2(2)-3 (putting co-ordinates of point of contact)
=4-3
=1

Answer 2

find the derivative of the equation.

or try puting in the values when u have eq in terms of x and y
and u'll find x, y

if mean slope by gradient then its rise over run wich is y/x