Question 475578
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(9,6\right)]. So this means that {{{x[1]=9}}} and {{{y[1]=6}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(1,4\right)].  So this means that {{{x[2]=1}}} and {{{y[2]=4}}}.



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula.



{{{m=(4-6)/(1-9)}}} Plug in {{{y[2]=4}}}, {{{y[1]=6}}}, {{{x[2]=1}}}, and {{{x[1]=9}}}



{{{m=(-2)/(1-9)}}} Subtract {{{6}}} from {{{4}}} to get {{{-2}}}



{{{m=(-2)/(-8)}}} Subtract {{{9}}} from {{{1}}} to get {{{-8}}}



{{{m=1/4}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(9,6\right)] and *[Tex \LARGE \left(1,4\right)] is {{{m=1/4}}}




The slope of any line perpendicular to this one will have a slope that is a negative reciprocal of this one. So simply flip the fraction and change the sign to get {{{-4/1=-4}}}



So the perpendicular slope is {{{-4}}}