Answer:
y = -1/2(x) - 4
Step-by-step explanation:
Two lines are perpendicular when both gradients multiplied is -1 (m₁*m₂ = -1)
To write the equation of a line perpendicular to y = 2x - 5 we first use this concept to find the gradient.
2m₂ = -1
m₂ = -1/2
Now we want to make sure this line passes through the point (2, -5)
In order for this to be true, there needs to be an offset (variable c)
So,
-5 = -1/2(2) + c
-5 = -1 + c
-4 = c
Now we have the gradient and offset, we write our equation in form of y = mx + c
y = -1/2(x) - 4