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## Lesson 8: Linear functions

Current time:0:00Total duration:2:43

# Linear graphs word problem: cats

CCSS Math: HSF.IF.B.4

## 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.