Main content

### Course: 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

© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# 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.

## Want to join the conversation?

- help me understand what varation mean(1 vote)
**variation**|ˌve(ə)rēˈāSHən|*noun***1**a change or difference in condition, amount, or level, typically with certain limits:*regional variations in house prices*|*the figures showed marked variation from year to year.*

•**Astronomy**: a deviation of a celestial body from its mean orbit or motion.

•**MATHEMATICS**: a change in the value of a function due to small changes in the values of its argument or arguments.

• (also magnetic variation) the angular difference between true north and magnetic north at a particular place.

•**Biology**: the occurrence of an organism in more than one distinct color or form.**2**a different or distinct form or version of something:*hurling is an Irish variation of field hockey.*

•**Music**: a version of a theme, modified in melody, rhythm, harmony, or ornamentation, so as to present it in a new but still recognizable form:*there is an eleven-bar theme followed by seven variations and a coda*| figurative :*variations on the perennial theme of marital discord.*

•**Ballet**: a solo dance as part of a performance.**DERIVATIVES**

variational |-SHənl|adjective**ORIGIN**late Middle English (denoting variance or conflict): from Old French, or from Latin*variatio(n-)*, from the verb*variare*(see vary) .(14 votes)

- Why don't you divide 30 divided by 6, so do 45 divided by 9? It is much easier.(9 votes)
- Yup. That's correct but when the questions get harder the other method makes it both clearer and easier to understand(11 votes)

- can we do this math differant way.i think this way is little travel for me.(3 votes)
- how would I do it if it was NOT an example of direct variation?(2 votes)
- Sorry, I would like to know if there are ways to solve this type of variation questions:

If x+y ∝z , when y is constant and z+x ∝y , when x is constant, then prove that, x+y+z ∝yz , where x, y, z are variables

I feel like I'm guessing randomly every time :/

Thanks a lot :D(1 vote) - What if we are only given the y/x value?(1 vote)
- how do find y in direct variation? could you please show me an example.(1 vote)
- The example that its giving in the video it kind of help me but in one part I don't really understand it like I'm kind of confused.(1 vote)
- what do you do when the y isnt divisible by the x(1 vote)
- this is a second (the same) question from you. There is never a case when y isnt divisable by the x. If you have such case please share it with us.(1 vote)

- im lost how do you find the constant variation of {(-5,3),(-5,1)(0,0)(10,-2)(1 vote)

## 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.