A Circle with center (-4,2) has a line tangent to it at (-2,6). Find the equation of the tangent.

I want to check if i got the right answer for this question.

I found the slope of the line of both points which came out to be .

Since the the line is tangent the slope would be the reciprocal of which is -2.

Plug in the slope with the points of the tangent (-2,6)... and I got the equation .

Does this seem right? It just looks like it's too easy...