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If the two variables in direct variation are X and Y then K is Y/X and this gives the equation Y = KX

Equivalently, if you write C = 1/K, then the constant of variation can be calculated as X/Y and this gives the equation as X = CY.

It does not matter which of the two you do as long as you use the correct resulting equation. Because of the relationship between K and C, one of them (at least in terms of school maths) will usually be an integer and so easier to work with.

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What is direct variation and how would solve direct variations?

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Can The graphs of two different direct variations can be parallel?

No, the graphs of two different direct variations cannot be parallel. Direct variation is represented by the equation ( y = kx ), where ( k ) is the constant of variation. For two direct variations to be parallel, they would need to have the same slope, which means they would have the same value of ( k ). However, since the variations are different, they must have different values of ( k ), resulting in non-parallel graphs.


How are direct variation and joint variation related?

Both are variations of certain kinds of equations. X=kY is a direct variation since X varies directly as Y and k is the constant of variation. X=k/Y is an inverse variation where X varies inversly as Y and k is the constant of variation. Both of these variations are also functions.


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Yes, all direct variations are linear functions. Direct variation describes a relationship where one variable is a constant multiple of another, typically expressed in the form (y = kx), where (k) is a non-zero constant. This equation represents a straight line through the origin on a graph, confirming that direct variations are indeed linear functions.


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