For two lines to be perpendicular to one another their slopes must be negative reciprocals of each other, mathematically:
m1*m2=-1
Since the slope of y=3x-10 is 3, the perpendicular line must have a slope of:
3*m=-1, m=-1/3
So the other line so far is:
y=-x/3+b, now you use the point (9,-7) to solve for the y-intercept, or "b"...
-7=-(-7)/3+b
-7=7/3+b
-7-7/3=b
(-21-7)/3=b
b=-28/3
so the perpendicular line to y=3x-10 passing through the point (9,-7) is:
y=(-x-28)/3
