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  • - [Instructor] We're told Glen drained the water

  • from his baby's bathtub.

  • The graph below shows the relationship

  • between the amount of water left in the tub in liters

  • and how much time had passed in minutes

  • since Glen started draining the tub.

  • And then they ask us a few questions.

  • How much water was in the tub when Glen started draining?

  • How much water drains every minute?

  • Every two minutes?

  • How long does it take for the tub to drain completely?

  • Pause this video and see if you can answer any or all

  • of these questions based on this graph right over here.

  • All right, now let's do it together.

  • And let's start with this first question.

  • How much water was in the tub when Glen started draining?

  • So what we see here is when we're talking about

  • when Glen started draining,

  • that would be at time t equals zero.

  • So time t equals zero is right over here.

  • And then so how much water is in the tub?

  • It's right over there.

  • And this point, when you're looking at a graph,

  • often has a special label.

  • If you view this as the y-axis,

  • the vertical axis as the y-axis

  • and the horizontal axis as the x-axis,

  • although when you're measuring time,

  • sometimes people will call it the t-axis.

  • But for the sake of this video, let's call this the x-axis.

  • This point at which you intersect the y-axis

  • that tells you what is y when x is zero?

  • Or what is the water in the tub when time is zero?

  • So this tells you, the y-intercept here tells you how much,

  • in this case, how much water we started off with in the tub.

  • And we can see it's 15 liters

  • if I'm reading that graph correctly.

  • How much water drains every minute?

  • Every two minutes?

  • Pause this video.

  • How would you think about that?

  • All right, so they're really asking about a rate.

  • What's the rate at which water's draining every minute?

  • So let's see if we can find two points on this graph

  • that look pretty clear.

  • So right over there at time one minute,

  • looks like there's 12 liters in it, in the tub.

  • And then at time two minutes, think there's nine liters.

  • So it looks like as one minute passes,

  • so we go plus one minute,

  • plus one minute, what happens to the water in the tub?

  • Well, it looks like the water in the tub goes down by,

  • went from 12 liters to nine liters.

  • So negative three liters.

  • And this is a line, so that should keep happening.

  • So if we forward another plus one minute,

  • we should go down another three liters,

  • and that is exactly what is happening.

  • So it looks like the tub is draining

  • three liters per minute.

  • So draining

  • three liters per minute.

  • And so if they say every two minutes,

  • well, if you're doing three liters per every one minute,

  • then you're going to do twice as much every two minutes.

  • So six liters every two minutes.

  • Two minutes.

  • But all of this, the second question,

  • we were able to answer by looking at the slope.

  • So in this context, y-intercept to help us figure out,

  • well, where did we start off?

  • The slope is telling us the rate

  • at which the water in this case is changing.

  • And then they ask us how long does it take

  • for the tub to drain completely?

  • Pause this video and see if you can answer that.

  • Well, the situation in which the tub has drained completely,

  • that means the there's no water left in the tub.

  • So that means that our y-value,

  • our water value is down at zero.

  • And that happens on the graph right over there.

  • And this point where the graph intersects the x-axis,

  • that's known as the x-intercept.

  • And in this context, it says,

  • hey, at what x-value do we not have any of the y-value left?

  • The water has run out.

  • And we see that happens at an x-value of five,

  • but that's giving us the time in minutes.

  • So that happens at five minutes.

  • After five minutes, all of the water has drained.

  • And that makes us a lot of sense.

  • If you have 15 liters

  • and you're draining three liters every minute,

  • it makes sense that it takes five minutes

  • to drain all 15 liters.

- [Instructor] We're told Glen drained the water

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B1 中級

傾き、x-切片、y-切片の文脈での意味|代数学I|カーン・アカデミー (Slope, x-intercept, y-intercept meaning in context | Algebra I | Khan Academy)

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    林宜悉 に公開 2021 年 01 月 14 日
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