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## Algebra (all 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

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# 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(4 votes)
- Khan Academy has a video about the difference between direct and inverse variation.

https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebra-direct_inverse_variation/v/direct-and-inverse-variation(3 votes)

- Is this a direct variation? 8x+9y=10(5 votes)
- 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).(8 votes)

- 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?(4 votes) - 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(3 votes)
- 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.(5 votes)

- 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.(2 votes)- 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 :-)(5 votes)

- If y2 varies directly with x2 does that mean y must vary directly with x(3 votes)
- w varies jointly as x,y, and z. if w=36 when x=2, y=8, and z=12, find w when x=1, y=2, and z=4

I need help with this one please(3 votes) - what is direct variation?(2 votes)
- Does it matter what you take as x or y ? If it does , then on what basis do you assign the variables?(2 votes)
- why am i here on earth pls tell me(2 votes)

## Video transcript

So, in this problem, they're telling us in
outer space, the distance an object travels varies directly with the
amount of time that it travels. And, that's of course assuming that it's
not accelerating, and there's no net force, and all of that on
it. So, I guess they're talking about a
specific object. So, some specific object, the amount, the
distance that it travels is directly, it varies directly, it varies directly
with the amount of time that it travels. So, if we think of in, in, in terms of constants of proportionality, and direct
variation, we could say that the distance, we could say that the distance
is equal to some constant, times the time, times the
time that it travels. The distance varies directly with the
amount of time that travels for this particular
object. If an asteroid travels 3000 miles, in, if
the asteroid travels 3000 miles in 6 hours, what is the
constant of variation? So the distance is 3000, so we have d is
equal to 3000 miles. We have 3,000 miles is the distance, and
that's going to be equal to the constant of
variation. The constant of variation times the time,
times 6 hours. So, if we wanna solve for the constant of variation, we can just divide both sides
by 6 hours. 6 hours, and we divide the right-hand side
by 6 hours. And, so, 3,000 divided by 6 is 500, and 6
divided by 6 is 1. The hours also cancel out if you care
about the units. And, so, the concept of proportionality,
the left-hand side is just 500, 500, and then we have miles per hour,
miles per hour. Fired 500 miles per hour, and that is
equal to k. So, the constant proportionality is 500
miles per hour, or you could say 500 if you're not too worried
about the units. Or, we should say, the constant of
variation, to use the terminology that they actually use
in the question.