The maximum number of points that lie on the graph of a linear equation in two variables is

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Two

Infinite

Three

None of these

answer is B.

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Detailed Solution

Here, we have to find the maximum number of points that lie on the graph of a linear equation in two variables.
An equation of the form

a x + b y + c = 0,

where a, b and c are real numbers such that

a ≠ 0

and

b ≠ 0,

is called a linear equation in two variables.
The graph of every linear equation in two variables is a straight line and every point on the graph the straight line represents a solution of the linear equation.
Thus, every solution of the linear equation can be represented by a unique point on the graph of the equation.
Therefore, the linear equation in two variables has infinitely many solutions.
Thus, the maximum number of points that lie on the graph of a linear equation in two variables is infinite.
Hence, option (2) is correct.

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