Explanation:
the slope is always the factor of x and the ratio
y coordinates difference / x coordinates difference
when going from one point on the line to another.
in short : y/x
the perpendicular slope is -x/y.
the ratio is turned upside down, and the sign is flipped.
so, the begin of our equation is
y = (1/3)x + b
b (the y-intercept, which is the y-value when x = 0) we get by using the given point and is coordinates:
-7 = (1/3)×6 + b = 2 + b
b = -9
so, the whole equation is
y = (1/3)x - 9