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Slope and intercept meaning in context

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- [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.