Question

Assertion: The graph of the equation of the form $y=mx$ is a line which always passes through the origin.

Reason: A linear equation in two variables has infinitely many solutions.

Which of the following is correct?

• A. A is true and R is false.
• B. A is false and R is true.
• C. Both A and R are true and R is the correct explanation of A.
• D. Both A and R are true and R is not the correct explanation of A.

Answer 1

The correct option is D

Both A and R are true and R is not the correct explanation of A.

Explanation for the correct option:

Step 1. Checking the truth of assertion

The equation is $y=mx$.

We can rewrite it as:

$$\begin{gathered} y=mx \\ \Rightarrow y-mx=0. \end{gathered}$$

Now, in order to pass through the origin, the equation must have $(0,0)$ as its solution.

Putting $(0,0)$ in the equation:

$$\begin{gathered} y-mx=0 \\ \Rightarrow 0-m\times 0=0 \end{gathered}$$ which is true.

Hence, the line passes through the origin and the assertion is true.

Step 2. Checking the truth of reason statement

A linear equation in two variables can be represented as: $ax+by=c$

This equation will be a straight line cutting through $x$-axis and $y$-axis.

It will have infinite length and therefore infinite number of solutions.

Hence, the reason is true.

Step 3. Checking if assertion and reason are related.

The reason statement is not explaining why or how the line $y=mx$ will pass through the origin. Instead, the reason statement is discussing about the infinite number of solutions in a linear polynomial.

Thus, the assertion and reason are true but not related to each other.

Hence, the correct option is D.