Question 582687
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-3,-3\right)]. So this means that {{{x[1]=-3}}} and {{{y[1]=-3}}}.

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



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



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



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



{{{m=(-2)/(8)}}} Subtract {{{-3}}} from {{{5}}} to get {{{8}}}



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



So the slope of the line that goes through the points *[Tex \LARGE \left(-3,-3\right)] and *[Tex \LARGE \left(5,-5\right)] is {{{m=-1/4}}}