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=(1)/(3) x+7`

Explanation:

We need to find the equation of a line perpendicular to
`y=-3x-3`, which passes through the point (-3, 6).

Recall that a line perpendicular to a line of the form:
`y=mx+b`, must have a slope which is the opposite of the reciprocal of the slope of the original line. that is, a slope of the form;

`slope=-(1)/(m)`

Then, in our case, since the original line has slope "-3", a perpendicular line to it should have a slope given by:

`slope=-(1)/(-3) =(1)/(3)`

We now know the slope, and also a point for this new line, so we use the point-slope form of a line:

`y-y_0=m_\perp\,(x-x_0)\\y-6=(1)/(3) (x-(-3))\\y-6=(1)/(3) x+(3)/(3) \\y-6=(1)/(3) x+1\\y=(1)/(3) x+7`