Question

Find the equation of the line through (9,−6) that is perpendicular to the line y=−x9−6.

Answer 1

The line equation is either y=-9x-6 or y=-x/9-6. It cannot be -x⁹-6, because this is a curve, not a line.

y=-9x-6. The slope of the perpendicular is 1/9 so its equation is y+6=(x-9)/9, y=x/9-1-6, y=x/9-7.

y=-x/9-6. The slope of the perpendicular is 9 so its equation is y+6=9(x-9),  y=9x-81-6, y=9x-87.