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Linear graphs word problem: cats

Sal finds the y-intercept and the slope of a linear relationship representing someone accumulating cats! He then interprets what the y-intercept and the slope mean in that context. Created by Sal Khan.

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  • blobby green style avatar for user Kody Allen
    I really can't seem to grasp all of these equations, how do i tell whether or not a graph represents a linear function?
    (7 votes)
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    • mr pants teal style avatar for user IanS
      Basically if you have two variables and no exponents, then you are dealing with a linear equations. Exponents would signify that you are dealing with some sort of curve, possibly a parabola in the case of a quadratic. Also if you have just a single variable and still no exponents and are being asked to graph it as a line on a two dimensional grid, then you are dealing with a vertical or horizontal line. For instance x = 1 is a vertical line that crosses x at 1. While y = 2 is a horizontal line that crosses y at 2.
      (12 votes)
  • leafers tree style avatar for user Kelli Medina
    Hi, I'm looking for a video or an explanation for something like this but a little different, with two independent variables and one dependent variable, for example, a club is selling hats for twelve dollars and sweatshirts for 26 dollars, write a function that represents the total amount the club can earn selling these? I have a vague idea for this but I'm not entirely sure, nor if I can use this method for this problem. Can anyone help, please?
    (6 votes)
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  • male robot johnny style avatar for user Caleb Cho
    After 10 years how many cats would she have? wow...
    (6 votes)
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  • leafers seedling style avatar for user jacob.pie
    how can you accumulate 30 cats in the time period of FIFTEEN DAYS. Calm down Jordan. They need to invest in some time to make their questions more reasonable.
    (5 votes)
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  • duskpin sapling style avatar for user 1_Lazarus, Lauren
    What about problems that don't have multiple choice answers?
    (5 votes)
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  • scuttlebug yellow style avatar for user Kenzzzzzzzzzzie
    In this video, he puts the change in cats over the change in time. Would it work to put the change in time over the change in cats? I've seen a few places where they put the change in time on the bottom, but is that always true or can you swap it around?
    (3 votes)
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    • boggle green style avatar for user Arya
      If you did it the other way by putting change in time on the bottom you would get per half a day she would get one cat. Therefore, per day you would get 2 cats. It does seem to work for this question but I'm not entirely sure if it works for every example.
      (1 vote)
  • winston default style avatar for user killergod2394thesecondbestfortniteplayer
    this will probably help me with my work on math
    (2 votes)
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  • aqualine ultimate style avatar for user Brian Nguyen
    What is the triangle before the variables c & t?
    (2 votes)
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  • leafers ultimate style avatar for user Evan Baxter
    You know the first three dimensions are up, right, and forward, but what is the fourth?

    Time! But time only goes one direction at a constant rate perceived differently by different people. If you speed up, slow down, or go backward at any speed, that is the fifth dimension-time travel!

    If you on purpose or accidentally do something wrong that shouldn't have happened, like playing on the swing when the timeline said you were supposed to play on the slide, then you have parallel or alternate dimensions-the sixth dimension. And if the universe were to go kablooie, it wouldn't fall apart-in fact, you wouldn't even know it happened. You would just be frozen in time for all of eternity. What is the seventh?
    (1 vote)
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  • piceratops sapling style avatar for user Eliza
    This may be a good time to bring up the fact that animal hoarding is a serious issue and not to be taken lightly.
    (1 vote)
    Default Khan Academy avatar avatar for user

Video transcript

Jordan is a cat enthusiast. She currently cares for several cats, but she just can't say no to adopting another cute little face. After moving into a bigger house, Jordan started adopting cats at a constant rate. The number of cats in Jordan's house, C, as a function of time since she moved in days, T, is plotted below. So this Jordan, she just keeps adopting cats. Her house is just getting more and more and more full of cats. I guess that's got to stop at some point. But for this question, they just say she keeps adopting them at a constant rate. So let's look at the choices here and see which of these statements is true. Jordan had 10 cats when she moved. So let's see this is time from when she moved in. So time equals 0 is right when she moved in her house. And it does look like, yes, she had 10 cats right where she moved in. So that first part of the statement is true. And after moving, she adopted 2 cats each day. So let's see the rate at which she's adopting cats. And I'm going to find another point on here. So we know that the point 0 comma 10 is on here. So on day 0, when time equals 0, she already had 10 cats, which seems to be more than enough for me. But let's see how many she gets to. So all of these other ones, it's hard to read. Well, it looks like here, this is definitely on day 15. On day 15, she had 40 cats. So let's see. After 15 days, when her change in time was 15, what was the change in her number of cats? Well, she went from 10 cats to 40 cats. So she went up to her change in the number of cats-- and we could call that delta C-- is equal to-- she went from 10 to 40. Her change in cats is 30. So her change in cats over change in time is 30 over 15. Or you could say, 2 cats per unit time, per day. So it does look like she got 2 cats per day. After 15 days at 2 cats a day, she had 30 more cats. She went from 10 to 40. So this statement looks right. And this one is multiple choice. So these other ones are probably wrong. But let's verify that. Jordan had 3 cats when she moved. Well, that's not true. 3 would have been right around here. So that's not right. Jordan had 10 cats when she moved. And after moving, she adopted 1 cat every 2 days. Well, that would be 1/2 a cat a day. And we know that that's not the case. She adopted 2 cats a day. After 15 days, she had 30 cats. So this isn't right either. Jordan had 3 cats where she moved. Well, we already know that that's not the case. So we know it's the first choice.