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## 8th grade

### Unit 3: Lesson 9

Linear models- Linear graphs word problems
- Modeling with tables, equations, and graphs
- Linear graphs word problem: cats
- Linear equations word problems: volcano
- Linear equations word problems: earnings
- Modeling with linear equations: snow
- Linear equations word problems: graphs
- Linear equations word problems
- Linear function example: spending money
- Linear models word problems
- Fitting a line to data

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# Linear graphs word problem: cats

CCSS.Math:

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.

## Want to join the conversation?

- 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)
- $38 because it equals it when adding it up(1 vote)

- After 10 years how many cats would she have? wow...(6 votes)
- The equation of the line is: y = 2x + 10 where x = time in days and y = cats. 10 years is equal to 10(365) = 3650 days. So if we plug 3650 days in for time we would get y = 2(3650) + 10

which makes y = 7310 cats.(8 votes)

- 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)
- A graph that represents a linear function should always have a straight line.

The equation of a linear functions is y=mx+b. So if you saw an equation that was y=3x+6. Then you’d know that the equation is a linear equation. If you were told to graph that equation, I guarantee you that the line on the graph would be a straight line.

Hope this helps and sorry for sending it 7 years late 😅(2 votes)

- 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)
**Sal wrote this question like this by purpose to make it more fun**.(4 votes)

- What about problems that don't have multiple choice answers?(5 votes)
- 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)
- 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)

- What is the triangle before the variables c & t?(2 votes)
- The Greek letter Delta, which means "change in". It describes the differences between two variables, the distance between two x values for example.(0 votes)

- this will probably help me with my work on math(2 votes)
- 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) - 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)

## 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.