Write the equation of a line perpendicular to y = 2x – 5 that passes through the point (2,-5).

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