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.
