Let's analyze the assertion and the reason to determine their correctness and the relationship between them.

Assertion:

There are infinite number of lines which pass through (3, 2).

• This is true. A point on a plane can be part of infinitely many lines because you can draw a line in any direction that passes through that point. For example, lines with equations like $y = mx + c$, where $c = 2 - 3m$ and $m$ is any real number, will pass through the point (3, 2).

Reason:

A linear equation in two variables has infinitely many solutions.

• This is also true. A linear equation in two variables (like $ax + by = c$) represents a line in the Cartesian plane, and all the points (solutions) on that line satisfy the equation. Since a line contains infinitely many points, the equation has infinitely many solutions.

Checking the relationship between Assertion and Reason:

• The assertion and the reason are both true, but the reason does not directly explain the assertion. The reason talks about the solutions of a linear equation, while the assertion is about the number of lines passing through a given point. The reason could be misleading if interpreted as the explanation for why there are infinitely many lines through a single point.

Conclusion:

• Assertion is true.
• Reason is true.
• Reason is not the correct explanation for the assertion.

Would you like more details, or do you have any questions?

Here are 5 related questions to consider:

1. How do you find the equation of a line passing through two given points?
2. What is the general form of a linear equation in two variables?
3. How can you determine if two lines are parallel or perpendicular?
4. How do you find the slope of a line given two points on the line?
5. Can a linear equation ever have a finite number of solutions? Under what conditions?

Tip: Always check if the reasoning provided directly explains the statement made in the assertion when solving assertion-reasoning questions.