Is this correct? if not can you explain why..

The equation of the line is: 2y = -x + 8

Step-by-step explanation:

The product of slopes of two perpendicular lines is -1.

The general equation of the line is y = mx + b

where, 'm' is the slope of the line.

Comparing this with the given equation: y = 2x - 3,

we see that the slope of the line is 2.

⇒ Slope of the line perpendicular to this line should be -.

We have the slope of a line and a point passing through it. So we can use the one - point from to determine the equation of the line.

One point form is: y - y₁ = m(x - x₁)

where, (x₁, y₁) is the point on the line.

Here: (x₁, y₁) = (-4, 6)

Therefore, the equation would be:

y - 6 = (x -  (-4)) $

⇒ 2y - 12 = -x - 4

⇒ 2y = - x + 8