Answer:
Option (2)
Step-by-step explanation:
Given equation of a line → y = [tex]\frac{1}{2}x+3[/tex]
Slope of the line 'm₁' = [tex]\frac{1}{2}[/tex]
Let the equation of a line perpendicular to the given line is,
y = m₂x + b
Here, m₂ = Slope of the perpendicular line
b = y-intercept
By the property of perpendicular lines,
m₁ × m₂ = -1
Therefore, [tex]\frac{1}{2}\times m_{2}=-1[/tex]
m₂ = -2
Equation of the perpendicular line will be,
y = -2x + b
Since the perpendicular line passes through a point (-3, 4)
4 = 6 + b
b = -2
Therefore, equation of the perpendicular line wiil be,
y = -2x - 2
Option (2) will be the answer.
