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# Slope and intercept meaning in context

Practice determining which feature of a linear model (the slope, the x-intercept, or the y-intercept) is useful for answering a given question in context.

## Want to join the conversation?

• is slope run over rise or rise over run
• it is rise over run
• Who is Flynn and why should I care?
• You should care because this decides your future. The point isn't to use slopes, although those are useful in life. You should care because this is how problem solving is tested.
• So I understand both lessons, but I can't seem to understand the first practice (Relating linear contexts to graph features), the second one is very clear to me (Using slope and intercepts in context). Could someone explain it so I can better understand it?
• **********************************Hard Question**********************************
What if John loaned Flynn 28 dollars? And Flynn's salary per week is 3 dollars. And every week the loan increases by 0.078 percent until Flynn paid every single dollar. How long will it take for Flynn to pay John back? And how much will it cost him at last?
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(1 vote)
• By pure algebraic manipulation I can't find a solution because the equation is of the form:

D = D_0*(1+r)
D_0*(1+r) = -3t + 28
Where D_0 = previous value of D.
r is the weekly interest rate.
t is the time in weeks.
This could be solved by iterations if I understood you correctly, Flynn is only allowed to pay 3\$ per week and AFTER he has paid, the weekly interest applies. First example of the iteration is:

D = 28
D_0 = 28 - 3 = 25
D = D_0*(1+7.8/100) = 25*(1.078) = 26.95
D_0 = 26.95-3=23.95
D = 23.95*1.078=25.82
... So on and so forth.

Then we can measure the time in weeks spent up to 0\$ or below even to know long will it take to pay back. The total amount spent is greater than 28\$:
P = 3*t
A little less actually, because the last week Flynn is going to pay <= 3\$ (very small probability of paying exactly 3\$), the last equation is good aproximmation regardless.
The answer for a 7.8% (that is what I think you meant) is 15 weeks and 44.93\$ spent int total.

If it is 0.078% (way too low weekly interest rate), 10 weeks and 28.09\$ total spent.

Compared to the easy version which is only: 28/3 = 9.33 weeks or 10 weeks realistically.

A simple program in c++ or python works for the iterative approach... now, I couldn't come up with an analytic one maybe someone could.

Good problem!
• Rise over run
• Did Flynn have to pay interest? Just kidding :)
• you're telling me that it took him four weeks to pay off twenty bucks?
• The scenarios are used for example purposes, and not meant to have any deeper meaning.
(1 vote)
• Could a payment plan that had interest be plotted with a line?
• Yes, as long as it isn't compound interest (which is a curve).

If you had a loan (l) of \$1000 with a simple 10% interest rate (i) being paid back in 12 monthly payments (p), you would use the following equation to get the total \$ amount due:
l + l(i * p)
Which with the above information would be:
\$1000 + \$1000(0.10 * 12) = 2200
From here you can simply graph a line with x being monthly payments made, and y being the remaining debt.

I hope this helps!