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

Slope and intercept meaning in context


Video transcript

flin sister loaned him some money and he paid her back overtime 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 alright now let's go through each of 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 and went from fifteen dollars to ten dollars so when we had plus one weeks in time our loan went down by five dollars 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's is 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 or another way to think about it that tells us that says what is 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 is past 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 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 equals zero when the horizontal variable is equal to zero we see that Flynn owes 20 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 did he know initially we'll rule that one out and we already picked one choice so we could rule out none of the above