Question

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

Answer 1

The equation of the new path would be y=1/3x+4.

Explanation
If two lines are perpendicular, their slopes are negative reciprocals of each other.  The original equation is written in slope-intercept form, y=mx+b, where m is the slope.  In this equation, m=-3=-3/1.

In the new equation, the slope would be the opposite sign and flipped; this means it would be 1/3.

We can use the point given, the slope and slope-intercept form to write the equation of the new line:

y=mx+b
3=1/3(-3)+b
3=1/3(-3/1)+b
3=(-3/3)+b
3=-1+b

Add 1 to both sides:
3+1=-1+b+1
4=b

This makes the equation y=1/3x+4.