Rate increases with either increase in enzyme or substrate concentrations (with a few caveats). So imagine your enzyme is capable of turning over 5 substrate molecules per second with a single enzyme molecule. And imagine that you only have a single enzyme molecule in solution (unrealistic, but this is a thought experiment). Now, you add another enzyme molecule. You are capable of turning over 10 substrate molecules per second. Finish this experiment to its logical conclusion and you can see that you should see a linear increase in rate with increasing enzyme concentration.
The caveat is that there has to be vast excess of substrate present. If you run out of substrate, adding more enzyme won't help.
