Question

A walking path across a park is represented by the equation y = -4x + 10. A new path will be built perpendicular to this path. The paths will intersect at the point (4, -6). Identify the equation that represents the new path.

Answer 1

Answer:
`y=(1)/(4)x-7`

Explanation:

The perpendicular slope of the line(m) =
`-(1)/(m)`:

• m = -4 ⇒
  `-(1)/(m) =-(1)/((-4)) =(1)/(4)`

The function formula is y = mx + b, where the y-intercept(b) is found by substituting in the values of a point on the line ⇒ (4, -6):

`y=(1)/(4)x+b\\-6=(1)/(4)(4)+b\\-6=1+b\\b=-6-1=-7`

So the perpendicular equation is
`y=(1)/(4)x-7`.