A drawing illustrating the first definition given would look something like this:
As h → 0 {\displaystyle h\to 0} , the slope of the line between ( a , f ( a ) ) {\displaystyle (a,f(a))} and ( a + h , f ( a + h ) ) {\displaystyle (a+h,f(a+h))} approaches the slope of the tangent line at x = a {\displaystyle x=a} .