
English: 
- [Instructor] When you hear
constant of proportionality,
it can seem a little bit
intimidating at first.
It seems very technical.
But as we'll see, it's a
fairly intuitive concept,
and we'll do several
examples and hopefully
you'll get a lot more comfortable with it.
So let's say we're trying to
make some type of baked goods,
maybe it's some type of muffin,
and we know that depending
on how many muffins
we're trying to make,
that for a given number of eggs,
we always want twice as many cups of milk.
So we could say cups of milk,
cups of milk, that's going to be equal to
two times the number of eggs.
So what do you think the constant
of proportionality is here,
sometimes known as the
proportionality constant?
Well yes, it is going to be two.
This is a proportional relationship
between the cups of milk
and the number of eggs.

Korean: 
비례상수라는 단어를 들었을 때
처음에는 무서워 보였습니다
전문적인 용어로 느껴지거든요
하지만 이제 보다시피
이것은 직관적인 개념입니다
몇 가지 예제를 풀어보면서
이해하길 바랍니다
머핀을 굽고 있다고 합시다
머핀을 굽고 있다고 합시다
머핀을 만들 때
머핀을 만들 때
달걀의 2배만큼
우유가 필요합니다
우유 컵의 수는
우유 컵의 수는
달걀 수의 2배입니다
따라서 여기서의 비례상수는
따라서 여기서의 비례상수는
따라서 여기서의 비례상수는
2가 되겠죠
우유와 달걀 사이의
비례상수입니다
우유와 달걀 사이의
비례상수입니다

Korean: 
우유 컵의 수는
항상 달걀 수의
2배입니다
주어진 달걀의 수에
비례상수를 곱하여
우유 컵의 수를 구합니다
표를 만들어서
비례관계를 더 쉽게
파악해 봅시다
달걀의 수
우유 컵의 수
표를 만듭니다
달걀이 1개 있다면
우유는 몇 컵 필요한가요?
1 × 2 = 2컵이 필요합니다
1 × 2 = 2컵이 필요합니다
달걀이 3개 있다면
2를 곱하여 구합니다
그러면 우유 6컵이 나오겠죠
달걀이 1000000개 있다면
엄청 큰 숫자죠
머핀 공장이 필요하겠네요
우유 몇 컵이 필요할까요?
1000000 × 2컵이 필요합니다
1000000 × 2컵이 필요합니다
즉 2000000컵입니다

English: 
The cups of milk are always
going to be two times
the number of eggs.
Give me the number of eggs,
I'm going to multiply it
by the constant of proportionality
to get the cups of milk.
And we can see how this is
a proportional relationship
a little bit clearer if we set up a table.
So if we say number of eggs
and if we say cups of milk
and make a table here,
well if you have one egg,
how many cups of milk
are you gonna have?
Well this right over here
would be one times two,
well you're gonna have two cups of milk.
If you had three eggs, well
you're just gonna multiply
that by two to get your cups of milk,
so you're gonna have six cups of milk.
If you had 1,000,000 eggs, so
we have a very big party here,
maybe we're some sort of
industrial muffin producer,
well how many cups of milk?
Well you put 1,000,000 in right over here,
multiply it by two, you
get your cups of milk.
You're going to need
2,000,000 cups of milk.

English: 
And you can see that this is
a proportional relationship.
To go from number of eggs to cups of milk,
we indeed multiplied by two every time.
That came straight from this equation.
And you could also see,
look whenever you multiply
your number of eggs by a certain amount,
you're multiplying your cups
of milk by the same amount.
If I multiply my eggs by 1,000,000,
I'm multiplying my cups
of milk by 1,000,000.
So this is clearly a
proportional relationship.
Let's get a little bit
more practice identifying
the constant of proportionality.
So let's say I'll make it
a little bit more abstract,
let's say I have some variable a
and it is equal to five
times some variable b.
What is the constant of
proportionality here?
Pause this video and see
if you can figure it out.
Yes, it is five.
Give me a b, I'm gonna
multiply it by five,
and I can figure out what a needs to be.
Let's do another example.
If I said that y is equal to

Korean: 
이것이 바로 비례관계입니다
달걀의 개수에
항상 2를 곱하면
우유 컵의 수가 나옵니다
이것도 방정식으로부터
나온 결과입니다
달걀의 수에
특정 값을 곱할 때마다
달걀의 수에
특정 값을 곱할 때마다
우유 컵의 수에도
같은 값을 곱합니다
달걀의 개수에서
1000000을 곱하면
우유 컵의 수에도
1000000을 곱합니다
따라서 틀림없는
비례관계라고 할 수 있죠
비례상수와 관련된
다른 문제를 더 풀어봅시다
좀 추상적인 문제입니다
변수 a가 있고
변수 b가 있습니다
a = 5b
여기서 비례상수는 무엇일까요?
강의를 멈추고
스스로 해보세요
네, 5입니다
주어진 b에 5를 곱하여
a를 구합니다
다른 예제로 갑시다
y = πx 에서

English: 
pi times x, what is the constant
of proportionality here?
Well you give me an x, I'm gonna
multiply it times a number,
the number here is pi, to give you y.
So our constant of
proportionality here is pi.
Let's do one more.
If I were to say
that y is equal to 1/2 times x,
what is the constant of proportionality?
Pause this video.
Think about it.
Well once again, this is
just going to be the number
that we're multiplying
by x to figure out y.
So it is going to be 1/2.
In general, you might sometimes
see it written like this.
y is equal to k times x,
where k would be some
constant that would be
our constant of proportionality.
You see 1/2 is equal to k here,
pi is equal to k right over there.
So hopefully that helps.

Korean: 
비례상수는 무엇일까요?
주어진 x에 π를 곱하면
y가 나옵니다
따라서 비례상수는 π입니다
하나만 더 풀어보죠
y = (1/2)x 에서
y = (1/2)x 에서
비례상수는 무엇일까요?
멈추고 한번 생각해 보세요
멈추고 한번 생각해 보세요
이 값을 x에 곱하면
y가 나옵니다
이 값을 x에 곱하면
y가 나옵니다
따라서 1/2입니다
일반적으로
이렇게 나타낼 수 있습니다
y = kx
여기서 상수 k는
비례상수입니다
여기서는 k = 1/2
여기서는 k = π 입니다
도움이 되었길 바랍니다
