Question

A city planner is rerouting traffic in order to work on a stretch of road. The equation of the path of the old route can be described as y = 2/5x− 4. What should the equation of the new route be if it is to be perpendicular to the old route and will go through point (P, Q)?
y − Q = -5/2(x − P)

y − Q = 2/5(x − P)

y − P = -5/2(x − Q)

y − P = 2/5(x − Q)

Answer 1

Answer:

y - Q = -5/2(x - P)

Step-by-step explanation:

The equation of a line in point slope form is expressed as y - y0 = m(x-x0)

(x0, y0) is the point

m is the slope

Given the equation

y = 2/5x− 4.

Slope m  = 2/5

Slope of the perpendicular line = -1/(2/5) = -5/2

Point;

x0 = P

y0 = Q

Substitute into the formula;

y - y0 = m(x-x0)

y - Q = -5/2(x - P)

This gives the required equation