How do I work out the equation of a tangent line to a curve?

A tangent line to a point of a curve is the straight line which is parallel to the the curve at that point.The equation of any straight line has equation form : y-y_1 = m(x-x_1) where m is the gradient of the line and (x_1,y_1) is ANY point on the linetherefore all we need to do is:find a point on the tangent line. Suppose we want to the find the equation of the tangent line to a curve at the point x=5. Then substitute x=5 in the equation of the curve and we have a point on the line!Calculate the gradient (slope) of the tangentThis is calculated by differentiating the equation of our curve then substituting the x-coordinate at which we wish the work out the tangent equationsubstitute m and (x_1, y_1) into the straight line equation and rearrange.