We can start with a single formula #y=Mx+b#. This is used in the case of only one variable being changed at a constant rate (e.g. a cost per item).
#M# is your "cost per" (or slope, but in the cases of buying and selling, it means the same). Since a soda costs #$0.75#, #M# can be replaced with #0.75#.
With this information, we can say,
#y=0.75x+b#
#b# is your "base value" (it may also be referred to as a #y#-intercept). In this situation, it is not too easy to define a base value because it isn't really a base value, it's just a single change in the total outcome. Your base value is from your coupon, which takes away #$0.50# from the total cost of the purchase. Since the #$0.50# is taken away, #b# is #-0.50#. When #b# is a negative, you can subtract the value rather than add.
So now we get,
#y=0.75x-0.5#
As for the #x# and the #y#. The #y# is the outcome of the change in the #x#, and the #x# is typically what can easily be changed in the given problem. So, #x# is the number of sodas (#n#) and #y# is the total cost (#c#).
So we end up with,
#c=0.75n-0.5# where #c# is your total cost in dollars and #n# is the number of sodas bought.
Sorry if this is a bit lengthy, but I hope it helped. Cheers, and best of luck to you!
