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## Algebra (all content)

### Unit 13: Lesson 7

Direct and inverse variation- Intro to direct & inverse variation
- Recognizing direct & inverse variation
- Recognize direct & inverse variation
- Recognizing direct & inverse variation: table
- Direct variation word problem: filling gas
- Direct variation word problem: space travel
- Inverse variation word problem: string vibration
- Proportionality constant for direct variation

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# Proportionality constant for direct variation

Worked example: y is directly proportional to x, and y=30 when x=6. Find the value of x when y=45. Created by Sal Khan and Monterey Institute for Technology and Education.

## Video transcript

y is directly proportional to x. If y equals 30 when
x is equal to 6, find the value of
x when y is 45. So let's just take this
each statement at a time. y is directly proportional to x. That's literally
just saying that y is equal to some
constant times x. This statement can
literally be translated to y is equal to some
constant times x. y is directly proportional to x. Now, they tell us, if
y is 30 when x is 6-- and we have this constant
of proportionality-- this second statement
right over here allows us to solve
for this constant. When x is 6, they
tell us y is 30 so we can figure out
what this constant is. We can divide both
sides by 6 and we get this left-hand side is
5-- 30 divided by 6 is 5. 5 is equal to k or
k is equal to 5. So the second sentence tells us,
this gives us the information that y is not just k
times x, it tells us that y is equal to 5 times
x. y is 30 when x is 6. And then finally, they say, find
the value of x when y is 45. So when y is 45 is
equal to-- so we're just putting in 45 for y--
45 is equal to 5x. Divide both sides
by 5 to solve for x. We get 45 over 5 is 9, and
5x divided by 5 is just x. So x is equal to 9 when y is 45.