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

Lesson 7: Direct and inverse variation

# Direct variation word problem: filling gas

Worked example: Model a context about filling gas with a direct variation equation. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• why do we always have to set X?
• "x" is the horizontal line in a cartesian plane. "x" and "y" are the most commonly used variables, though "x" is prefered more. Hope that helped :)
• when point p moves at a speed of x cm per second and the time taken to reach point b after starting point a is y seconds, express the relation between x and y as an equation.

y= blank/x how do find the constant of variation.
• Jed,
There are lots of letters in your question points p (which is moving) and points a and b as well as x cm/second speed and y seconds.
Thats a lot of letters, but to answer the question you need one more letter.
Let "d" be the distance point p has traveled after y seconds.

The cm/second * seconds = cm * (seconds/seconds). The seconds over seconds cancel out giving you an answer in cm. (words can cancel just like numbers)

If you multiply x cm/second * y seconds you get xy cm as your answer.
And this answer would be equal to the distance (d) in cm that point p has traveled after y seconds.
so d cm = x cm/second * y seconds. so
d=xy which can be converted to
d/x = y or
y=d/x which you had as y=blank/x
The blank is the distance that point p has traveled.

I hope that helps.
• Why is the constant called k? Why not c?
• It abbreviates the German word “konstante” which means… you guessed it: constant. Also, the letter 'c' is used for many other tasks and is usually not available.
• Is the constant of variation the same as slope?
• Couldn't you just get the answer to this question faster by dividing 18 by 2.25 and just skipping all the "Oh so Y is this and X is this now time to solve"?
• Definitely! But Sal wants us to understand the process of actually solving this problem, since in real life, you come upon much more complex problems.
• can a direct variation be vertical on the x-axis
• I see the quick answer without much calculation, i.e. 18/2.25 = 8, Now I tried to think more structured as the solution suggested at the video, sorry, but this time I don't get where does the 9/4 fraction come from? Checking the tutorials here at Khan Academy have been really helpful to clear my doubts in math problems. Appreciate your answer. Many thanks to the team!
• The 9/4 fraction comes from the conversion of 2.25 into a fraction. When it is converted, it becomes 2 1/4 and when it becomes an improper fraction, it becomes 9/4 (because 2*4=8, then 8+1=9)
(1 vote)
• Hi my name is Grace and I have a quiz on this on wednesday and I really need help! I am very confused and don't know what to do.Can you give me some help??