Correct Answer - Option 2 : x + 2y = 12
Concept:
y = mx + b, is the equation of the line, where m = slope of the line and b = y-intercept of the line.
- If two lines are parallel, then their slopes are equal, m1= m2.
- If two lines are perpendicular to each other then the product of there slopes is equal to -1, m1m2= -1.
Equation of line passing through point (x1, y1) and whose slope is m , (y - y1) = m (x - x1).
Calculation:
Equation of given line is , 2y = 4x +3
∴ y = 2x + \(\frac{3}{2}\)
On comparing with standard equation , y = mx + c, slope of line is 2 .
As we know that , if lines are perpendicular to each other , m1m2= -1.
Then slope of line passes through point (2,5) and perpendicular to the given line is - \(\frac{1}{2}\)
∴ Equation of line is , (y - 5) = - \(\frac{1}{2}\) (x - 2)
⇒ 2y -10 = -x + 2
⇒ x + 2y = 12 .
The correct option is 2.
