Is this a proportional relationship?

Question

Lets say Ralph opened a savings account with a deposit of $100. Every month after that, he deposited $20 more. Is this proportional?

Answer 1

No this is not a proportional relationship.  To see this, make a table of months versus money

 

Months     Money

    0           100

    1           120

    2           140

    3           160

    4           180 

 

and so on.  Now look at the ratio (or proportion) between the 2 variables in each month.  

 

In month 1 Money / Months = 120/1 = 120

In month 2 Money / Months = 140/2 = 70

In month 3 Money/  Months = 160/3 = 50 1/3 

 

In a proportional relationship these ratios would all be the same.  Since they are different this is not a proportional relationship.  

 

On a slightly more advanced note, one of the requirements of a proportional relationship is that it forms a straight line through the origin, that is y = mx with the y-intercept equal to 0.  So if Ralph had opened his account with 0$ his pattern would form a proportional relationship.