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Is it true that a linear equation determines a line in the x-y plane

User Bondolin
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Answer:

True

Explanation:

A linear equatin in the xy plane contains two variables x and y and the power of both x and y should always be 1

The std form of a linear equation is

ax+by+c =0

Let us prove that this repesents a straight line only.

Consider the equation ax+by+c=0

Differentiate wrt x

a + b y' =0

Or y' = -b/a

In other words the slope of the curve is not dependent on the points taken but constant.

This ensures constant variation of y over x.

Hence this is nothing but a straight line in xy plane.

User Drew Frezell
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