Applying intercepts and slope
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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.