Which of the following equations is an example of inverse variation between the variables x and y

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um So you don't have your equations to give an example of an inverse variation, but when you have an inverse variation, You have y equals some number, I'm just gonna say five divided by X. Um An inverse variation is where one variable goes up and the other variable goes down. So as X increases, Y decreases. Um So notice this would be an universe variation. That means if I multiply both sides by X X times Y equals five would also be an example of an inverse variation, and if I solved it for X X equals five over why would also be an example of an inverse variation? Um I hope it helps.

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Northern Michigan University

Amber M.

Algebra

7 months, 3 weeks ago

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which of the following equations is an example of inverse variation between the variable x and y?

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Video Transcript

um So you don't have your equations to give an example of an inverse variation, but when you have an inverse variation, You have y equals some number, I'm just gonna say five divided by X. Um An inverse variation is where one variable goes up and the other variable goes down. So as X increases, Y decreases. Um So notice this would be an universe variation. That means if I multiply both sides by X X times Y equals five would also be an example of an inverse variation, and if I solved it for X X equals five over why would also be an example of an inverse variation? Um I hope it helps.

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While direct variation describes a linear relationship between two variables , inverse variation describes another kind of relationship.

For two quantities with inverse variation, as one quantity increases, the other quantity decreases.

For example, when you travel to a particular location, as your speed increases, the time it takes to arrive at that location decreases. When you decrease your speed, the time it takes to arrive at that location increases. So, the quantities are inversely proportional.

An inverse variation can be represented by the equation x y = k or y = k x .

That is, y varies inversely as x if there is some nonzero constant k such that, x y = k or y = k x where x ≠ 0 , y ≠ 0 .

Suppose y varies inversely as x such that x y = 3 or y = 3 x . That graph of this equation shown.

Since k is a positive value, as the values of x increase, the values of y decrease.

Note: For direct variation equations, you say that y varies directly as x . For inverse variation equations, you say that y varies inversely as x .

Product Rule for Inverse Variation

If ( x 1 , y 1 ) and ( x 2 , y 2 ) are solutions of an inverse variation, then x 1 y 1 = k and x 2 y 2 = k .

Substitute x 1 y 1 for k .

x 1 y 1 = x 2 y 2 or x 1 x 2 = y 2 y 1

The equation x 1 y 1 = x 2 y 2 is called the product rule for inverse variations.

Example:

In a factory, 10 men can do the job in 30 days. How many days it will take if 20 men do the same job?

Here, when the man power increases, they will need less than 30 days to complete the same job. So, this is an inverse variation.

Let x be the number of men workers and let y be the number of days to complete the work.

So, x 1 = 10 , x 2 = 20 and y 1 = 30 .

By the product rule of inverse variation,

( 10 ) ( 30 ) = ( 20 ) ( y 2 ) 300 = 20 y 2

Solve for y 2 .

y 2 = 300 20 = 15

Therefore, 20 men can do the same job in 15 days.

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