Which situation represents an example of a non-proportional relationship?
A. A restaurant charges $1.75 for each soft drink.
B. A cell phone company charges customers 10 cents per text sent or received.
C. A gym charges a membership fee of $50, plus a monthly charge of $20 per month.
D. A dog walker charges $10 to walk one dog for 30 minutes.

I think it is c.

So a non-proportional relationship is basically a line that does not cross the origin of a graph. So using the linear exhaustion of a line, y=mx+b, a PROPORTIONAL RELATIONSHIP would be something along the lines of y=mx+0 because b, which is the w intercept is 0. If the y intercept is 0 then the line will cross the origin of the graph. So with this being said a NO -PROPORTIONAL RELATIONSHIP would be anything that has a b value besides 0, because then the line would cross at a y intercept besides the origin.

So with this being said the equation of a line for:
a) would be y=1.75x (because it is only charging per drink, and nothing else, there is no b value or y intercept). This means this is a PROPORTIONAL RELATIONSHIP, crossing the origin (THIS IS NOT THE ANSWER)
b) would be y=0.10x (because it is only charging per amount of texts, and nothing else, there is agin no b value, so the y intercept is 0, crossing the origin). (THIS IS ALSO NOT THE ANSWER)

C) would be y=20x+50 (x is the number of months, which then determine the amount of money you spend at the gym based on how many months you go there. Plus, you have to add in the cost of the gym membership as well, being 50$. So, in this case because 50 is being added to the 20x, the b value or y intercept would be 50. This WOULD NOT cross the origin because the intercept is not 0, as a result THIS IS YOUR ANSWER)!

d)(this one I don’t exactly know how to explain... but I don’t think you can really make a proper linear equation because it is dealing with time (30min) but also money (10 for one dog). In this case you would have to have a variable for the number of dogs and the amount of time your dog(s) are walked (30 min). So in this case, the equation y=10x+30z (let’s say d is the number of dogs and s is the number of 30 min increments), The equation would not make sense because you are working with two different things... time and money in the same equation. You cannot add the 30minutes plus 10$ because that is combining two different units. So with this, I don’t think this is the answer. (I’m sorry about this one, I don’t know for sure if this is the right explanation for this or not, but I don’t think this is the correct option. I think c would be)!

I hope this helps!!! :)
Good luck!