Question 644570
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(5,-8\right)]. So this means that {{{x[1]=5}}} and {{{y[1]=-8}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(3,-3\right)].  So this means that {{{x[2]=3}}} and {{{y[2]=-3}}}.



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



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



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



{{{m=(5)/(-2)}}} Subtract {{{5}}} from {{{3}}} to get {{{-2}}}



{{{m=-5/2}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(5,-8\right)] and *[Tex \LARGE \left(3,-3\right)] is {{{m=-5/2}}}


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