Hello, Lucas.
A line has a standard form of y=mx+b. m is the slope of the line: how quickly y changes as x is changed, also known as the "rise(y) over the run(x)." b is the y intercept -- the value of y when x=0.
A perpendicular line has a slope that is the negative inverse of the original line. Our original line is y = -3X-2. The slope is -3, so the perpendicular line will have slope of -(1/-3), or 1/3.
The new line becomes y = (1/3)x + b. We need to find b. We're in luck, since we are given a point that the line goes through. If we input those values of x and y, we can solve for b:
y = (1/3)x + b
2 = (1/3)9 + b
2 = 3 + b
b = -1
The equation becomes y = (1/3)x - 1
Try graphing the two equations, and you'll see what's happening.
Bob
