You I am sure have heard of the point slope form yeah? so adapting that we replace which makes sense since if you evaluate a function at a point it gives the y co-ordinate...next we replace which is the x co-ordinate lastly we need the slope at the point we want the tangent curve to go through which is and to get the slope of at we need to find ...giving us the adapattion of hte pointslope formula the tangent line equation and that is how/why we use the tangent line...any more questions just ask