Question

Assertion: The graph of every linear equation in two variables need not be a line.

Reason: Graph of a linear equation in two variables is always a line.

Now, choose the correct option.

• A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
• B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
• C. If Assertion is correct but Reason is incorrect.
• D. If Assertion is incorrect but Reason is correct.

Answer 1

The correct option is D

If Assertion is incorrect but Reason is correct.

Step 1: Explanation for the assertion

Assertion: The graph of every linear equation in two variables need not be a line.

An equation of the form $ax+by+c=0$, where $a\ne 0,b\ne 0$, $c$ is a real number, is called a linear equation with two variables. By solving an equation of this type, we can say, a linear equation with two variables has infinitely many solutions. As every point is a solution of the graph, the graph will be a straight line.

Hence, the assertion is incorrect.

Step 2: Explanation for the reason

Reason: Graph of a linear equation in two variables is always a line.

The graph of a linear equation in two variables will be a straight line, as every point is a solution of the graph.

Hence, the reason is correct

Step 3: Finding if the assertion and reason are related

Hence we conclude that the given assertion is incorrect but the reason is correct.

Therefore, the correct answer is option D.