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Question
Prove that every straight line has an equation of the form Ax + By + C = 0, where A, B and C are constants.
Solution
Given a straight line
Either it cuts the y-axis, or is parallel to or coincident with it.
We know that the equation of a line which cuts the y-axis (i.e., it has y-intercept) can be put in the form y = mx + b; further
If the line is parallel to or coincident with the y-axis
Its equation is of the form x = x1
Where x = 0 in the case of coincidence.
Both of these equations are of the form given in the problem and hence the proof.
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