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## Applying intercepts and slope

Current time:0:00Total duration:2:20

# Slope and intercept meaning in context

## 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.