From the line y=3x-10 find the equation of the line that is perpendicular to this line and goes through the point 9,-7

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

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