A student has developed a money-saving strategy that uses the formula $S = 450 + 100r$.
a) Give a possible interpretation of his strategy.
I don’t really know if my initial interpretation really makes sense. I thought maybe $S = {}$savings. 450 could possibly be the part of his weekly salary that he saves already, and 100 could represent the amount he gets paid when he works overtime, then $r$ could represent how much overtime he works.
b) What do the slope and $S$-intercept of the graph of the relation represent, based on the interpretation from part a)?
Would the slope in this case represent the increase each time in money he is saving? And then the $S$-intercept represents when he starts saving?
Is there a better way to represent this formula?
a) One possible interpretation is that the student makes an initial deposit of USD 450 into his account, on the same day he gets his paycheck. Out of each successive paycheck he deposits USD 100 into the account. The $r$ is the number of paychecks he has gotten after the initial deposit.
b) The slope of the graph is 100 and represents the deposit amount for each paycheck. The S-intercept is 450 and represents the initial deposit.
That is one possible interpretation. There are others, of course. You are correct that "the slope in this case represent the increase each time in money he is saving." You are wrong that "the s-intercept represent[s] when he starts saving". The S-intercept is not a time, it is an amount: the initial amount, in fact. So you could edit what you wrote to "the s-intercept represents the amount when he starts saving."