Question 582563
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(6,3\right)]. So this means that {{{x[1]=6}}} and {{{y[1]=3}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(5,8\right)].  So this means that {{{x[2]=5}}} and {{{y[2]=8}}}.



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



{{{m=(8-3)/(5-6)}}} Plug in {{{y[2]=8}}}, {{{y[1]=3}}}, {{{x[2]=5}}}, and {{{x[1]=6}}}



{{{m=(5)/(5-6)}}} Subtract {{{3}}} from {{{8}}} to get {{{5}}}



{{{m=(5)/(-1)}}} Subtract {{{6}}} from {{{5}}} to get {{{-1}}}



{{{m=-5}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(6,3\right)] and *[Tex \LARGE \left(5,8\right)] is {{{m=-5}}}