Correct Answer - Option 1 : 3x + y - 2 = 0
Concept:
The general equation of a line is y = mx + c
Where m is the slope and c is any constant
- The slope of parallel lines is equal.
- The slope of the perpendicular line have their product = -1
Equation of a line with slope m and passing through (x1, y1)
(y - y1) = m (x - x1)
Calculation:
Given line x - 3y + 5 = 0
⇒ y = \(1\over3\)x + \(5\over3\)
⇒ Slope(m1) = \(1\over3\) and c1 = \(5\over3\)
Now for the slope of the perpendicular line (m2)
m1 × m2 = -1
⇒ \(1\over3\) × m2 = -1
⇒ m2 = -3
Perpendicular line has the slope -3 and passes through (2, -4)
∴ Equation of the perpendicular line is
(y - y1) = m (x - x1)
⇒ y - (-4) = -3 (x - 2)
⇒ y + 3x - 2 = 0