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## Algebra 1

### Course: Algebra 1 > Unit 4

Lesson 5: Applying intercepts and slope- Slope, x-intercept, y-intercept meaning in context
- Slope and intercept meaning in context
- Relating linear contexts to graph features
- Using slope and intercepts in context
- Slope and intercept meaning from a table
- Finding slope and intercepts from tables
- Linear equations word problems: tables
- Linear equations word problems: graphs
- Linear functions word problem: fuel
- Graphing linear relationships word problems

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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(12 votes)
- it is rise over run(9 votes)

- how will this effect spongebobs legacy?(15 votes)
- Who is Flynn and why should I care?(13 votes)
- 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.(3 votes)

- **********************************
**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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P.S. Please comment the answer down below :)(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!(14 votes)

- 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?

Thanks in advance :)(7 votes) - Did Flynn have to pay interest? Just kidding :)(6 votes)
- Rise over run(5 votes)
- Could a payment plan that had interest be plotted with a line?(2 votes)
- 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!(4 votes)

- i don't get it(2 votes)

## Video transcript

- [Instructor] Flynn's
sister loaned him some money, and he paid her back over time. Flynn graphed the relationship
between how much time had passed, in weeks, since
the loan and how much money he still owed his sister. What feature of the graph represents how long it took Flynn
to pay back the loan? Pause this video, see if
you can figure that out. All right, now let's go
through each of these choices. So the first one is the slope. So the slope tells us how much do we change in
the vertical direction for any given change in
the horizontal direction. So for example, if we start from here, we can see that if one week goes by, we go from one week to two weeks, we can see that our loan went down. It went from $15 to $10. So when we had plus one weeks in time, our loan went down by $5. And then that happens over the next week. And that rate of how
quickly the loan is paid, that's what the slope tells us. And it would be constant over the course of the entire time period
is what makes this a line, is that slope is always
going to be constant. So the slope is useful for the rate at which the loan is being paid back, but it's not the clearest
way to figure out how long it took Flynn
to pay back the loan. So I would rule that one out. The x-intercept, that's
where the graph intersects the horizontal axis, which is often referred to as the x-axis. Or another way to think about it, that tells us, that
says, what is the x-value when our vertical value, our
y-value, is equal to zero? And our y-value is the money owed. So it says, hey how much
time has passed when we owe, when we don't owe any more money or when Flynn doesn't owe
any more money to his sister? Well that's exactly
what they're asking for. How long did it take Flynn
to pay back the loan? And that's what that x-intercept tells us. It took him four weeks. After four weeks, he
didn't owe any more money to his sister. So I like this choice,
but let's just review the other ones. The y-intercept, well
that's where the graph intersects the y-axis right over there. This tells us what's going
on at time t equals zero. At time t equal zero or time equal zero, when the horizontal
variable is equal to zero, we see that Flynn owes $20. So this one isn't valuable
for figuring out when he, how long it takes to pay it back. This one is useful for figuring out how much did he owe initially. So we'll rule that one out. And we already picked one choice, so we can rule out none of the above.