To graph a rate or ratio from a table, how do you determine the scales to use on each axis

First determine how much room you have for each axis. Let's say you count your graph paper and it has 30 squares by 10 squares.

Then find the largest number in the x-values. If you want your graph long-ways, then plot the x-values on the longer length of the sheet, the side with 30 squares.
Let's say your largest x-value is 300. Then you divide that largest value (300) by how many squares are on the axis (30). 
300/30 = 10, so each square is 10.

Same thing goes for the y-axis. Say your largest y-value is 50. If the y-axis of your graph paper is 10 squares long, then each square would increase by
50/10 = 5.