Answer:
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 -[tex]\frac{1}{2}[/tex].
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 = [tex]$ - \frac{1}{2} $[/tex](x - (-4)) $
⇒ 2y - 12 = -x - 4
⇒ 2y = - x + 8
