Fit Km and Vmax from a table

You will write the Michaelis-Menten rate as a function, take reciprocals of a list, and fit a straight line to the double reciprocal plot. From the line you will read $V_{\max}$ and $K_m$.

The idea. The line $1/v = (K_m/V_{\max})\,(1/[S]) + 1/V_{\max}$ has a y-intercept $1/V_{\max}$ and a slope $K_m/V_{\max}$. A function line_fit that finds a slope and an intercept is already written for you.

Your tasks.

1. In rate, return the rate for a given vmax, km and substrate concentration s.
2. In reciprocals, return a list that holds 1 divided by each number of the list.
3. Fit the line to the reciprocals of substrate and measured, and set vmax_fit and km_fit.