Slope and intercept in tables

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. The slope tells us how much do we change in the vertical direction for any given change in the horizontal direction. 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 fifteen dollars to ten dollars. So when we had plus one week in time, our loan went down by five dollars. And then that happens over the next week. 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. What makes this align is that 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. Now, another way to think about it is that it tells us what is the x-value when our vertical value, our y-value, is equal to zero. Our y-value is the money owed. So it says, "Hey, how much time has passed when we owe—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 equals zero, or time equals zero, when the horizontal variable is equal to zero, we see that Flynn owes twenty dollars. 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 could rule out none of the above.