Question

explain why ax+by=c have only two arbitrary constant,and not three?
(where no condition is given like c not equal to 0)
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Answer 1

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$Therefore, the equation Ax + By + C = 0 represents a line with slope -A/B and y-intercept -C/B. In case B = 0, then the equation Ax + By + C = 0 will become. x = -C/A. This represents a line parallel to the Y axis (explained here).$