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

Lesson 7: Direct and inverse variation

# Direct variation word problem: space travel

Sal models a context about space travel with a direct variation equation. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• i dont understand difference between direct and inverse variation
• Is this a direct variation? 8x+9y=10
• No. In the equation 8x + 9y = 10, y does not vary directly with x. You need to have 8x + 9y = 0. Then 9y = -8x. Then 1y = (-8/9)*x. So the constant of variation is k = -8/9.
In summary, y = kx is called direct variation, whereas y = kx + c is just linear variation. Both y = kx and y = kx + c are lines when you graph them. But only y = kx goes through the origin = (0, 0).
• In direct variation, as x increases, does y always have to increase?

If the constant is negative, then y will decrease as x increases, right?
• I've seen the direct variation 1 video and direct variation application. I'm not completely understanding how to find direct variation in a problem such as x-3y=0
• It helps to put it in the standard form, so for your example:
x-3y=0
-3y = -x
y = x/3 which is also y = (1/3)x
Now that you have it in this form, it is easier to see that it maps to y=kx, a direct variation.
• hi i have a question..if any of you could please answer it, Btw, its for my test preparation.
a shopowner blends 3 types of tea, A,B and C, in the ratio 6:4:7. if the mass of tea C in the mixture is 28 kg, find the difference in the masses of the other two types of tea.
• Hi,
When you are dealing with ratios, remember that you are dealing with parts of a whole. With your ratio above, you have
6 parts of A,
4 parts of B, and
7 parts of C.
If you are then trying to figure out how much of each portion of the ratio you have, the easiest way to do it is to figure out what 1 part would equal.
If 28 kg of C represents 7 parts of the ratio, simply divide
28/7 and you know that 1 part equals 4 kg.
From there, you can multiply the other ratio values by 4 kg
6x4 = 24
to get the mass of A and
4x4 = 16
to get the mass of B.
Hope that helps :-)
• If y2 varies directly with x2 does that mean y must vary directly with x