Question

The equation of the straight line passing through the point (−1, 2) and perpendicular to the line $x + 3y = 4$ is:

• A. $x - y - 3 = 0$
• B. $3x + y + 1 = 0$
• C. $3x - y + 5 = 0$
• D. $3x - y + 10 = 0$

Hint:

A line perpendicular to $Ax + By = C$ is of the form $Bx - Ay = k$.

Answer 1

The Correct Option is C

Step 1: Concept
Slopes of perpendicular lines.

Step 2: Analysis
The slope of $x + 3y = 4$ is $m_1 = -1/3$. The slope of a perpendicular line is $m_2 = -1/m_1 = 3$.

Step 3: Calculation
Using point-slope form: $y - 2 = 3(x - (-1))$.
$y - 2 = 3x + 3 \implies 3x - y + 5 = 0$.

Step 4: Conclusion
The equation of the line is $3x - y + 5 = 0$. Final Answer: (C)