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### Course: Algebra (all content)>Unit 13

Lesson 7: Direct and inverse variation

# 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
ORIGIN late Middle English (denoting variance or conflict): from Old French, or from Latin variatio(n-), from the verb variare (see vary) .
• Why don't you divide 30 divided by 6, so do 45 divided by 9? It is much easier.
• Yup. That's correct but when the questions get harder the other method makes it both clearer and easier to understand
• can we do this math differant way.i think this way is little travel for me.
• how would I do it if it was NOT an example of direct variation?
• 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.