Question

The equation $ax+by+c=0$ represents a straight line ________.

• A. for all real numbers a, b and c
• B. only when $b \neq 0$
• C. only when $a \neq 0$
• D. only when at least one of a and b is non-zero

Hint:

A straight line always needs at least one variable to define a direction.

Answer 1

The Correct Option is D

Step 1: Concept
Definition of a linear equation in two variables.
Step 2: Analysis
If both $a$ and $b$ are zero, the equation becomes $c = 0$, which does not involve any variables and thus cannot represent a line in a 2D plane.
Step 3: Evaluation
For the equation to represent a locus of points forming a line, there must be at least one variable ($x$ or $y$) present with a non-zero coefficient.
Step 4: Conclusion
This requires $a^2 + b^2 \neq 0$, meaning at least one of $a$ or $b$ must be non-zero.
Final Answer:(D)