Functional Relationship

Question

Donald owes Jesse $306.24. He plans to pay Jesse $23.24 every week until his dept is paid off. Which equation best represents the relationship between the number of weeks Donald has spent paying off his dept,w, and the amount of money,m, Donald still owes Jesse?

Please Help and explain how you did it.

Answer 1

Cristina,

Think of the goal of the equation you're being asked to write as being that you can plug in a number for 'weeks' and find out how much money Donald still owes Jesse.

Here are the two important pieces of information to notice:

1. Donald is paying Jesse the same amount every week
2. You know that when weeks=0 (before Donald starts paying Jesse) that money=$306.24

#1 tells us that equation is linear, meaning it fits the for y=mx+b. In this case we're solving for

money = m(weeks)+b

#2 tells us that when we take that equation and plug in weeks=0 and money = $306.24 you get

$306.24 = m*(0 weeks) + b, therefore b=$306.24. Now you know that

money = m(weeks)+$306.24

where 'm' is some number which represents the slope of this line if you were to draw it on a graph.

If this is a multiple choice question, that might be enough information for you to eliminate all the wrong answers. If not, here's a simple way to solve for the slope in this question:

After one week, Donald will have paid Jesse $23.24, so

($306.24 - $23.24) = m(1 week)+$306.24

which can be solved for m=-23.24 $/week

Using the same symbols as your original question where m=money and w=weeks, that means the equation is:

m = (-23.24 $/week)w+$306.24

Simon