Answer
Option B is correct.
The equation of the line is
y + 12 = (-1/3) (x - 2)
Step-by-step explanation
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
So, we need to compute the slope of this line to solve it.
To do that, it should be noted that for two lines that are perpendicular to each other, their slopes are related through
(m₁)(m₂) = -1
For this question, the slope of the line given as y = 3x is 3.
So, we can calculate the slope of the line that we want.
m₁ = 3, m₂ = ?
(m₁) (m₂) = -1
3m₂ = -1
Divide both sides by 3
(3m₂/3) = (-1/3)
m₂ = (-1/3) = -⅓
So, for the line we want,
y - y₁ = m (x - x₁)
m = slope = -⅓
Point = (x₁, y₁) = (2, -12)
x₁ = 2
y₁ = -12
y - y₁ = m (x - x₁)
y - (-12) = (-1/3) (x - 2)
y + 12 = (-1/3) (x - 2)
Hope this Helps!!!