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## Operations and Algebraic Thinking 222-226

### Unit 1: Lesson 4

Identifying proportional relationships- Intro to proportional relationships
- Proportional relationships: movie tickets
- Proportional relationships: bananas
- Proportional relationships: spaghetti
- Identify proportional relationships
- Proportional relationships
- Proportional relationships
- Is side length & area proportional?
- Is side length & perimeter proportional?

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# Intro to proportional relationships

To know if a relationship is proportional, you should look at the ratios between the two variables. If the ratio is always the same, the relationship is proportional. If the ratio changes, the relationship is not proportional.

## Want to join the conversation?

- What if an odd and even number were in a proportional.(16 votes)
- If an odd and an even were in a proportional like 2:3 it would just be like 4:6(22 votes)

- (1.) Turn 23% into the decimal .23.

(2.) Multiply .23 and 80.

(3.) .23 X 80 = 18.4(24 votes)

- Can you make this more easier like more understandable?(10 votes)
- Proportions are the same ratios written in different forms. A proportional relationship is states that they are the same. For example, 1/2 and 6/12 have a proportional relationship, which means they are the same.

I hope this helps!!(6 votes)

- What is a rate?(1 vote)
- A rate is essentially a constant. This constant cannot and must not change. Like Jada posed the example, I will take it one step further: A car is going at 25 miles per five hours, find the unit rate; the unit rate is actually just someone compared to one. So for every one of that object, there are x number of the other(7 votes)

- What does constant of proportionality mean and why does it matter?(3 votes)
- It is the same thing as slope of a line IF the line goes through the origin (0,0). y=kx is the formula or k = y/x. Note that the general slope formula, m = (y2-y1)/(x2-x1) can be used with (0,0) to get m = (y2-0)/(x2-0) or m = k = y2/x2. It is always the same no matter which point on the line you choose, thus constant.(2 votes)

- Oh Please! I'm frustrated by this! I can't understand it!! Please I'm literally
**crying**out of frustration! I've got a test soon, please break this down into easy parts. It would be nice.(3 votes)- 6/2=3. 9/3=3. 3 is the constant of proportionality(1 vote)

- How do you write a equation that describes the relationship(3 votes)
- is there an easier way.

Thank You.(3 votes)- I guess the easier way is to re-watch the video until you understand it because this is the only method.(0 votes)

- this is boring(2 votes)
- I really can't understand this!!(2 votes)

## Video transcript

What I want to introduce you to
in this video is the notion of a proportional relationship. And a proportional relationship
between two variables is just a relationship
where the ratio between the two variables is always going to be the same thing. So let's look at an example of that. So let's just say that we want
to think about the relationship between x and y. And let's say that when x is one, y is three, and then
when x is two, y is six. And when x is nine, y is 27. Now this is a proportional relationship.
Why is that? Because the ratio between y and x
is always the same thing. And actually the ratio between y and x
or, you could say the ratio between x and y, is always the same thing. So, for example--
if we say the ratio y over x-- this is always equal to--
it could be three over one, which is just three.
It could be six over two, which is also just three. It could be 27 over nine,
which is also just three. So you see that y over x is
always going to be equal to three, or at least in this table right over here. And so, or at least based on
the data points we have just seen. So based on this, it looks like that
we have a proportional relationship between y and x. So this one
right over here is proportional. So given that, what's an example of
relationships that are not proportional. Well those are fairly easy to construct. So let's say we had-- I'll do it with
two different variables. So let's say we have a and b. And let's say when a is one, b is three. And when a is two, b is six. And when a is 10, b is 35. So here-- you might say look, look when a is one, b is three so the ratio b to a-- you could say b to a-- you could say well when
b is three, a is one. Or when a is one, b is three. So three to one. And that's also the case when b is six, a is two.
Or when a is two, b is six. So it's six to two. So these ratios
seem to be the same. They're both three.
But then all of sudden the ratio is different right over here. This is not equal to 35 over 10. So this is not a
proportional relationship. In order to be proportional
the ratio between the two variables always has to be the same.
So this right over here-- This is not proportional. Not proportional. So the key in identifying
a proportional relationship is look at the different values
that the variables take on when one variable is one value, and then what is the
other variable become? And then take the ratio between them. Here we took the ratio y to x,
and you see y to x, or y divided by x-- the ratio of y to x
is always going to be the same here so this is proportional. And you could
actually gone the other way. You could have said, well
what's the ratio of x to y? Well over here it would be one to three, which is the same thing as two to six, which is the same thing as nine to 27. When you take this ratio--
if you say the ratio of x to y instead of y to x, you see that
it is always one third. But any way you look at it--
the ratio between these two variables-- if you say y to x,
it's always going to be three. Or x to y is always going to be one third. So this is proportional
while this one is not.