Write an equation of the line perpendicular to given line

First, convert given equation of a line x – 2y – 6 = 0 into slope intercept form y = mx + c, where m is the slope of a line.
2y = x – 6
y = (1/2)x – 3

After comparing both equations, we get the slope m₁ = 1/2

Now, if m₂ is the slope of perpendicular line then condition two lines are perpendicular is m₁m₂ = -1 or m₂ = -1/m₁.
Since,
m₁ = 1/2
m₂ = -2

Now, we find the equation of a line which is passing through the point (a, b) and slope is m is y – b = m(x – a)

Here,
Point is (-3,2) and slope is m = -2, Therefore,
y – 2 = -2[x – (-3)]
y – 2 = -2[x + 3]
y – 2 = -2x – 6
y + 2x = -6 + 2
y + 2x = -4
2x + y = -4

Hence, the equation of a perpendicular line is 2x + y = -4.

CONCEPT TO DRAWING A GRAPH OF LINES