The equation of the line passing through point 
with slope
m is given by 
.
If you have a differentiable function y=f(x) and a particular value of x, say, x=c, then the slope of the tangent line when x=c is f'(c). Since the point on the graph at this value of x is (c,f(c), then the equation of the tangent line is (y-f(c))=f'(c)(x-c).