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### 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(15 votes)
- it is rise over run(13 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 :)(10 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) - Did Flynn have to pay interest? Just kidding :)(7 votes)
- Hello, this video makes sense, but the assignment has nothing to do with this, I can't figure out what the heck the assignment even is talking about. The assignment is: Relating linear contexts to graph features(3 votes)
- NOTE: i'm trying to reach some new badges, can you guys pls give this answer some upvotes? thx

btw im tryna reach 50+ upvotes

the assigment does have to do with the video, the assignment is asking you to find a relationship in the points. If you see how the x goes to the next number and how the y goes to the next number, you can see a pattern. The pattern is that whenever x changes by a specific value, y has to change by a specific value too. You should try to use the pattern until x or y reaches 0, then you will find the x or y intercept. Hope this helped!!(9 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!(5 votes)

- what is a intersept and what does it do.

(%)(1 vote)- Intercept is the point where the function touches the x-axis or y-axis.

For example, if you have a function modelling time of studying versus the result. Time should be the x-axis, and result should be the y-axis. You want to know when a person didn't study, what is their result. When a person didn't study, it means the time = 0, which is the y-intercept.(5 votes)

- He used the most easiest examples possible the practice test is way more complex than this.(1 vote)
- Examples are meant to help you understand the topic, and not demonstrating all possible cases.

You're expected to understand this topic, and solve the practice using your own knowledge.

If you find confusing on the topic, you can ask here.(5 votes)

- How do you find the slope in simpler terms?(3 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.