is this equation a direct variation? 8x + 9y = 10 if it is what is the constant of variation?

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A line that is a direct variation must be of the form y=mx, where m is the slope of the line.  This means, for the line 8x+9y=10, to determine if it is direct variation, then we need to rearrange it by isolating y.

`8x+9y=10`   move 8x term to right side

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A line that is a direct variation must be of the form y=mx, where m is the slope of the line.  This means, for the line 8x+9y=10, to determine if it is direct variation, then we need to rearrange it by isolating y.

`8x+9y=10`   move 8x term to right side

`9y=-8x+10`   divide both sides by 9

`y=-8/9x+10/9`

In this case, we see that the slope is `-8/9` , but there is a non-zero y-intercept, since `b=10/9` .

The line is a partial variation, and is not a direct variation.

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