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Current time:0:00Total duration:5:24

CCSS.Math:

we're told kaya rode her bicycle toward a tree at a constant speed the table below shows the relationship between her distance to the tree and how many times her front tire rotated so once her tire rotated four times she was twenty two and a half metres from the tree then when she's rotated eight times she's twelve and a half metres from the tree when it rotated twelve times then she's only two and a half metres to the tree so she's getting closer and closer there are more rotations that her tire has had so then they asked us some questions here so they asked us how far away was the tree to begin with how far does kaya travel with each rotation how many rotations did it take to get to the tree so like always pause this video and see if you can answer these questions on your own before we do it together so let's start with the first question how far away was the tree to begin with so the way that I would think about it is after four rotations we're 22 and a half metres from the tree we see that if we increase by another four rotations so let's see plus four rotations we see that we have gotten ten meters closer to the tree or our distance to the tree has gone down by 10 meters it's alright negative 10 meters here if we want to figure out how far the tree was to begin with we have to go back to 0 rotations so if we're going back by 4 so we're subtracting 4 from the rotations and 4 going at a constant rate well then we would add 10 meters so we would add 10 meters if we add 4 rotations we get 10 meters closer if we take away 4 rotations to get us back to 0 rotations then we will go 10 meters further so that would be at 32 point 5 meters so 32 point 5 meters is how far the tree was to begin with when Kara had 0 rotations the next question is how far does kaya travel with each rotation all right well we already saw that with 4 rotations she's traveling 10 meters so we could say 10 meters in 4 rotations so if we divide both of these by 4 what would we get well that's the same thing as two-and-a-half meters in one rotation so this is 2.5 meters and last but not least how many rotations did it take to get to the tree well we know that after 12 rotations she's only two and a half meters away from the tree we also know that in every one rotation she gets two and a half meters closer so she only needs one more rotation to cover this next two and a half meters so if we go plus one rotations we're going to go down two and a half meters we're going to go two and a half meters closer to the tree and we will be at the tree so how many rotations did it take to get to the tree in total 13 rotations now one thing that's interesting is to think about what we just did in a graphical context that you might have seen before and if we were to put on the horizontal axis rotations and if we were to put on the vertical axis distance to the tree distance to tree I'll just call the vertical axis the y axis and the horizontal axis the x axis well we could see here that we have 0 4 8 12 I could go to 16 and then we saw that at 0 rotations we are 32.5 meters from the tree so 32.5 this is all going to be in meters so this first question was really another way of asking what is our y-intercept and this next question how far does kaya travel with each rotation well we saw that when you increase irritations by 4 your distance to the tree goes down by 10 meters so when this is +4 we went down we went down 10 meters so it's negative 10 meters so really what we were thinking about right here this is could think about the magnitude of the slope the slope of this line the slope of this line that would describe her distance to the treat as based on the number of rotations the slope is going to be our change in our distance which is negative 10 for our change in rotations over 4 so the slope of this line is negative two point five meters per rotation but when they say how far does KY travel with each rotation she's getting two-and-a-half meters closer her distance goes her distance from the tree goes down by two-and-a-half meters and this last question how many rotations did it take to get to the tree well at what point is our Y value our just it to the tree zero and we saw that it is at 13 rotations so this is another way of thinking about what was the x-intercept so the line and it's a line because we know that she's traveling at a constant rate looks something like that so they really were thick asking us the y-intercept the slope and the x-intercept