Question

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.

Answer 1

y -6 = 1/3(x +3) or y = 1/3x +7

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