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# Slope, x-intercept, y-intercept meaning in context

CCSS.Math:

## Video transcript

we're told Glenn 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 Glenn started draining the tub and then they ask us a few questions how much water was in the tub when Glenn 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 could answer any or all of these questions based on this graph right over here alright now let's do it together let's start with this first question how much water was in the tub when Glenn started draining so what we see here is when we're talking about when Glenn 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 is the y axis and the horizontal axis is 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 am reading that graph correctly how much water drains every minute every two minutes pause this video how would you think about that alright so they're really asking about a rate what's the rate at which water is draining every minute so let's see if we can find two points on this graph that looked pretty clear so right over there at time 1 minute looks like there's 12 litres in it and in the tub and then at time 2 minutes I think there's 9 liters so it looks like as one minute passes so we go plus 1 minute plus 1 minute what happens to the water in the tub well it looks like the water and the tub goes down by went from 12 liters to 9 liters so negative 3 liters and this is a line so that should keep happening so if we forward another +1 minute we should go down another 3 liters and that is exactly what is happening so it looks like the tub is draining 3 liters per minute so draining draining 3 liters per minute and so if they say every 2 minutes well if you're doing 3 liters per every 1 minute then you're going to do twice as much every 2 minutes so 6 liters every 2 minutes 2 minutes but all of this the second question we were able to answer by looking at the slope so in this context y-intercept 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 asked 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 which the tub has drained completely that means that 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 you eat 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 is there the water has run out and we see that happens in an x value of 5 and but that's giving us the time in minutes so that happens at 5 minutes after 5 minutes all of the water is drained and that makes a lot of sense if you have 15 liters and you're draining 3 liters every minute it makes sense that it takes 5 minutes to drain all 15 liters