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### Course: 6th grade (Illustrative Mathematics) > Unit 6

Lesson 17: Lesson 17: Two related quantities, part 2# Ratios on coordinate plane

Ratios represent the relationship between two quantities and can be visualized on a graph. When the ratio is constant, the points form a straight line, illustrating the connection between the quantities. Examples include bakers using flour, car wash charges, and earnings from shoveling snow.

## Want to join the conversation?

- Does the x cordinate always come first(36 votes)
- Yes, X is always first... think about it as the alphabet x comes before y on the alphabet(96 votes)

- when do you use ratios and coordinates?(23 votes)
- marking location(5 votes)

- When do use this in real life?(5 votes)
- If you got stranded on an island, and all you had was a map, and a corded phone, you would need to call out your latitude and longitude, which is close enough to a grid.(28 votes)

- how much wood could a wood chuck chuck if a would chuck could chuck wood(7 votes)
- He would chuck, he would, as much as he could, and chuck as much wood as a woodchuck would if a woodchuck could chuck wood.(15 votes)

- Which kind of ratio should you use? Either 3;5 Say, or 3/5?(7 votes)
- 3/5 might be mistaken as a fraction(8 votes)

- i just dont understand anything bcause im just not smart(1 vote)
- Don't worry, you
**will**understand, it will just take some time and thinking through.

Let's look carefully at an example. Suppose a group of kids is invited to a party. Every kid is supposed to get two cookies each at the party. If**four**kids get invited, how many cookies would you have to make so that there are*just*enough cookies to give each child his or her two cookies? If you reply with the answer we can keep working through this.(21 votes)

- i don't have any questions(4 votes)
- why does he take so long to explain things(6 votes)
- Because some people need long explanations to fully understand what the video is about(0 votes)

- This was a good ratio and I liked it what i liked about it was it was kinda chrecky(5 votes)

## Video transcript

- [Instructor] We are told that a baker uses eight cups of flour to
make one batch of muffins for his bakery. Complete the table for the given ratio. So they're saying that for every batch, he needs eight cups of flour or he needs eight cups
of flour for every batch. So if you have two batches how many cups of flour would that be? Pause the video and try to figure it out. Well if he has twice as many
batches, he's gonna have twice the number of cups of flour. So instead of eight, it
would be 16 cups of flour. And if he had three times
the number of batches, it would be three times the
number of cups of flour. So instead of eight, it would
be eight times three, or 24. Now down here, they say
plot the ordered pairs x comma y from the table
on the following graph. So we wanna graph one batch, eight cups, two batches, 16 cups,
three batches, 24 cups. So let's do that. Let's see if we can, okay. So right here, I'm assuming
on the horizontal axis that is our batches, and
then our vertical axis is cups of flour. So for every batch, we
need eight cups of flour. So one batch, this is
eight right over here, five, six, seven, eight, and then for two batches,
we're going to need 16 cups of flour so that puts us right over there, that's 16. And then for three batches,
we are going to need 24 cups of flour, and that
actually goes slightly off of our screen here, let
me scroll up a little bit. So for three batches, we're
going to have to bring that to 24 which is right here and I can see the 25 right above that. And what you'll see,
because the ratio between our batches and our cups
of flour are constant, that all of these points,
you could connect them all with one straight line
because we have a fixed ratio. Every time we move one to the right, we're gonna move eight up. Every time we add another
batch, we're gonna have eight more cups of flour,
every time we add a batch, eight more cups of flour. Lets do another example. Here we're told Drew
earns money washing cars for his neighbors on the weekends. Drew charges a set rate
for each car he washes. The points on the
following coordinate plane show how much Drew charges
for two, five, and eight cars. So let's see what's going on over here. So when he washes two cars,
he looks like he charges $15. When he washes five cars,
it looks like he's charging, well it looks like some
place between 35 and $40, and he charges eight cars, it looks like he's charging $60. So one way to think about it is the ratio between the number of cars he's washing and the dollars, it stays at two to 15, notice two cars, for every $15. I guess I could say
$15 for every two cars. And so, when you go to eight cars, you're multiplying by
four the number of cars and you're also multiplying
by four the number of dollars. And so once again, since
we have a fixed ratio here, all three of these points
sit on the same line. But then they ask us down here, they say how much does
Drew charge for four cars? Well if it's $15 for two cars, well then four cars would be twice as much. So it would be $30 for four cars. We have the same ratio. Let's do one more example. Here we're told McKenna
earns money each time she shovels snow for her
neighbors, as she should. McKenna plots points on
the coordinate plane below to show how much she earns
for different numbers of times she shovels snow. Alright. So let's see, when she
shovels snow three times, looks like she gets,
halfway between 16 and 20, looks like she gets $18, four times, looks like it's $24, so looks like the ratio is
staying constant at three to 18. The ratio of three to
18 is the same thing as, one way to think about it
is $18 for every three times she shovels snow, that would
be equivalent of six dollars for every time she shovels snow. So let's go down here to
see what they're asking us. They say which of the
following ordered pairs could McKenna add to the graph? So this would be one
times she shoveling snow, would she get $10 for it. So does she get $10 for
every time she shovels snow? No, that wouldn't be
consistent with the data here. She got $18 for shoveling
snow three times. So that looks like she's
getting six dollars for every time she shovels snow. So I would rule out choice A, choice B, shoveling snow twice, she gets $12. Well that makes sense,
if she gets six dollars every time she shovels snow. If the ratio of shoveling of the times to the dollars is three
to 18 or one to six, that would be equivalent to two to 12 and we would pick that choice.