# How do you know if an equation #6x-5y=4# is a direct variation And if it is how do you find the constant of the variation?

See below.

Direct variation is expressed as:

We have:

rearranging:

So this does not represent direct variation.

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To determine if the equation 6x - 5y = 4 represents a direct variation, we check if it can be written in the form y = kx, where k is a constant.

If we rearrange the given equation into slope-intercept form (y = mx + b), and find that it matches the form y = kx, then it represents a direct variation.

To find the constant of the variation (k), we divide both sides of the equation by x (assuming x ≠ 0) to isolate y, then compare the coefficient of x to k.

So, in this case, we would rearrange the equation to solve for y:

6x - 5y = 4 -5y = -6x + 4 y = (6/5)x - 4/5

Comparing this to the form y = kx, we see that the coefficient of x is (6/5), which is the constant of the variation (k).

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