Question 293431
Where is the equation?
What are you talking about with 12.5 cents per gallon? We are told it is $1.60 a gallon not $.125 per gallon. 
What did you do with x=miles and y = allowance?

We are told " Determine and then plot a weekly savings equation for Irvin that represents earnings minus money spent on gas. Write a physical interpretation for both intercepts of the savings equation."
Each week he is given $10 but he spends 1.6 per gallon 
x=gallons
y= savings
earnings =$10
minus gas expense
y=10-(1.60*x)
The problem told you how to set it up.
"plot a weekly savings equation for Irvin that represents earnings minus money spent on gas."
The y intercept is the earnings. If he doesn't buy any gas (x) he can save $10
So if x=0 then  y=10

If he has no savings (y=0) then the cost of gas used up all his allowance 
So if y=0 then 1.60*x=10 which is the x intercept of x=10/1.60=10/1.6=100/16