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CCSS.Math:

we're told that Felipe feeds his dog the same amount every day from a large bag of dog food two weeks after initially opening the bag he decided to start weighing how much food remained in the bag on a weekly basis here's some of his data so we see after 14 days there's 14 kilograms remaining then after another 7 days passed by so now we're 21 days from the beginning there's only ten and a half kilograms left that after 28 days there are seven kilograms left all right so we're going to try to use this data to start answering some interesting questions and maybe we'll also try to visualize it with a graph so the first thing that we might try to tackle is well how much how much food was in the bag to begin with if we assume that he's using the same amount of food every week so pause this video and see if you can figure that out how much food was in the bag to begin with if we assume that Felipe is feeding his dog the same amount every week okay now there are several ways to do this but to help us visualize this let me see if I can graph the data that we have and then see what would happen as we approach the beginning of this of what's going on here the dog feeding and maybe as we go to the end as well so let's see this is my x-axis this is my y-axis I'm going to make x-axis measure the passage of the days so number of days on the x axis and on the y axis I'm going to measure I'm gonna measure food or remaining and that is in kilograms and let's see it looks like maybe if my scale goes up to let's make this 5 10 15 20 and then 25 I can make a little higher 25 I think this will be sufficient and then we want to go up to 28 days and it looks like they're measuring everything on a weekly basis so let's say that this is 7 7 14 21 and then 28 and they gave us some data points so after 14 days there's 14 telegrams remaining so 14 days there's 14 kilograms remaining right over there after 21 days there's ten and a half kilograms remaining 21 days ten and a half is right about there after 28 days there's seven kilograms remaining so after 28 days seven kilograms and we're assuming the rate of the dog food usage is the same that he's feeding his dog the same amount every week and so this would describe a line that the rate is going to be the slope of that line and then if we can plot this line if we know where that line intersects the x and y axes we might be able to figure out some other things so actually let me draw a line here let me see if I can use this little line tool to connect the dots in a reasonable a reasonable way so let's say it looks something like that that's our line that will describe how quickly he is using his dog food so let me make sure that this dot is should be on the line as well now let's try to answer that first question and think about how we might do it how much food was in the bag to begin with so what point here represents how much food was in the bag to begin with well that's the amount of food remaining at day zero at the beginning of this so that would be this point right over here would describe how much food was in the bag to begin with this would be the y-intercept y-intercept is when our x value is equal to zero what is our Y value and when we just look at it the graph it looks like it's a little bit over 20 but we could find the exact value by thinking about the slope which is thinking about the rate at which the dog food is being depleted we can see that every week every week that goes by or every seven days that goes by it looks like we use three and a half kilograms or another way to think about it every two weeks it looks like we use an entire kilogram so let me put it this way when we go plus 14 days plus 14 days it looks like we use up or the food remaining goes down by a goes down every two weeks our it goes down by seven kilograms seven kilograms negative seven kilograms so if we want to figure out this exact value we just have to reverse things if we are going back fourteen days then we're going to go up seven kilograms so if we were at 14 up seven kilograms this right over here is the point 0 comma 21 so how much food did Philippe start with in the bag 21 kilograms and we got that from the y-intercept now another question is how much is Philippe feeding his dog every day pause this video and see if you can figure that out well we know every 14 days he's feeding the dog 7 kilograms so one way to think about it is and we're really looking at the slope here to figure out the rate at which he's feeding his dog so the slope is equal to our change in the Y so negative 7 kilograms every hour change in the X every 14 days and so 7 over 14 is the same thing as 1/2 so this is equal to negative 1/2 of a kilogram per day so this tells us every day the food remaining is going down half a kilogram so that means he's feeding his dog assuming his dog is eating the food and finishing it that his dog is eating half a kilogram a day and if we wanted to ask another question how many days will the bag last how would you think about that and we know it's going to be out here someplace if we just continue that line because this point right over here where our line intersects the x-axis that would be our x intercept that is the x value when our Y value is zero and our Y is the amount of food remaining so we want to know what what day do we have no food remaining and we could try to estimate or we could figure out it exactly we know that every 14 days we use up 7 kilograms so if we are at 7 as we are right over here and we go 14 days in the future we should use up the remaining the remaining contents of the bag so plus 14 days we're going to use up the remaining seven kilograms and so this should happen 14 days after the 28th day so this is going to be the 42nd day