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 = two fifthsx − 4. What should the equation of the new route be if it is to be parallel to the old route and will go through point (Q, P)? ay − Q = negative five halves(x − P) by − Q = two fifths(x − P) cy − P = negative five halves(x − Q) dy − P = two fifths(x − Q)

Answer 1

Answer: D

Explanation:

The equation of a line in the point slope form is expressed as

y - y1 = m(x - x1)

where

m represents slope

x1 and y1 represents coordinates of the point that the line passes.

From the information given, the equation of the path of the old route is

y = 2x/5 - 4

Recall, the equation of a line in the slope intercept form is expressed as

y = mx + c

By comparing both equations,

slope, m = 2/5

If two lines are parallel, it means that they have the same slope. Given that the new route is to be parallel to the old route and will go through point (Q, P), then

m = 2/5

x1 = Q

y1 = P

The equation of the new route be

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