Ms. gibson made an initial deposit of $500 when opening a bank account. after the initial deposit, she deposited the same amount of money each month. the table below shows the total amount of money, a, she deposited into the account after a certain number of months, t, since opening it. write an equation to model the relationshipbetween t and a.

Let say the number of the months is t, the total amount of depo is a and a0 is the initial amount of money deposited. You can put it like this:
a= f(t) = a0 + x*t

You can solve the equation by inserting two of any t value. If you use f(8)-f(4) it will be
a0+ x(8)= 2500 
a0+ x(4)= 1500
-
8x- 4x= 1000
4x= 1000
x=250

Then the new equation would be:
a= a0 + 250*t
Putting f(4) value you can find a0
1500= a0+ 250*4
a0=1500-1000=500

The final equation would be
a= 1000+ 250*t