Acity water department is proposing the construction of a new water pipe, as shown. the new pipe will be perpendicular to the old pipe. write an equation that represents the new pipe.

I found a similar problem to your problem here, which is shown in the attached picture. So, from the picture, we have to find the equation for the red line. All we have to do is find two points of the line. That would be: Point 1(2,0) and Point 2(-2,3). The general equation would be:

y - y₁ = (y₂-y₁)/(x₂ - x₁) * (x - x₁)

Substituting the coordinates to the equation,

y - 0 = (3-0)/(-2 - 2) * (x - 2)
y = -3(x -2)/4
Rearranging,
4y = -3x + 6 or 4y + 3x = 6