A walking path across a park is represented by the equation y=-3x - 3.A new path will be built perpendicular to this path. The paths will intersect at
the point (-3,6). Identify the equation that represents the new path.

  y -6 = 1/3(x +3)   or   y = 1/3x +7

Step-by-step explanation:

The slope of the line describing the given path is the x-coefficient, -3. The slope of the perpendicular line will be the negative reciprocal of that:

  m = -1/(-3) = 1/3

The point-slope form of the equation for a line can be used to write the equation for the new path:

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

For m=1/3 and (h, k) = (-3, 6), the new path can be represented by ...

  y -6 = 1/3(x +3) . . . . point-slope form

  y = (1/3)x +7 . . . . . . slope-intercept form

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x