Calculus: Early Transcendentals 8th Edition

The instantaneous velocity is given by $$v(t)=\lim_{h\to0}\frac{f(t+h)-f(t)}{h}.$$ It can be interpreted as the slope of the tangent line of the graph of $f$ at the point $(t,f(t))$.
The instantaneous velocity says how much the position changes per unit interval of time in the limit when the length of this interval tends to zero which is $$v(t)=\lim_{h\to0}\frac{f(t+h)-f(t)}{h}.$$ Here the length we divided the small change in position $f(t+h)-f(t)$ with the small time interval $h$. This expression matches the definition of the slope of the tangent line of the graph of $f$ at the point $(t,f(t))$ so in terms of the graph of $f$, we interpret the instantaneous velocity as the slope of the tangent.