SOLUTION: you borrowed $112 from your sister and told her that you would pay $8 a week until the loan is paid. your brother borrowed $165 from your sister and told her he would pay $13.75 a

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Question 918195: you borrowed $112 from your sister and told her that you would pay $8 a week until the loan is paid. your brother borrowed $165 from your sister and told her he would pay $13.75 a week until the load is paid.
1. write a linear equation that represnets the balance of each loan. identify the slop and y-intercept of each equation and explain what they represent in the real-life situation.
2. use a graph to determine who will pay off their loan first. explain reasoning.
3. explain how you can verify your answer to part (b) algebraically.
4. explain the meaning of the intersection of the two lines in terms of the real-life situation.
5. after the third week, you decide to pay your sister $11 a week until the load is paid off. does this change your answer to part 2. explain reasoning.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +y+ = the unpaid balance of each loan ( amount still owed )
Let +x+ = the number of the week after the
loan is made ( which is week +0+ )
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Your equation:
(a) +y+=+-8x+%2B+112+
Your brother's equation:
(b) +y+=+-13.75x+%2B+165+
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(1)
y-intercept occur where +x+=+0+, so
(a) +y+=+-8%2A0+%2B+112+
(a) +y%280%29+=+112+
and
(b) +y+=+-13.75%2A0+%2B+165+
(b) +y+=+165+
The y-intercepts are the amount of each loan
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(2)
Here's the plots for each loan:
+graph%28+400%2C+400%2C+-2%2C+15%2C+-10%2C+200%2C+-8x+%2B+112%2C+-13.75x+%2B+165+%29+
The loans are paid off when each line hits the x-axis and
y-axis ( unpaid balance ) = 0
--------------------------------
(3)
You can just set +y+=+0+ and solve for +x+, which
is the week number when it will be paid
-------------------
(4)
The intersection is the week number when both owe your
sister the same amount
-----------------------
(5)
The loan gets paid off sooner, because the equation then
has a steeper slope and reaches the x-axis ( zero unpaid balance )
sooner
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