Question 189012
Since f(2)=-3, this means that we have the ordered pair (2,-3). This also means that if {{{x=2}}}, then {{{y=-3}}}



Also, since f(-2)=5 this means that we have the ordered pair (-2,5). This also means that if {{{x=-2}}}, then {{{y=5}}}



So this makes *[Tex \LARGE \left(x_{1}, y_{1}\right)] the first point *[Tex \LARGE \left(2,-3\right)] and *[Tex \LARGE \left(x_{2}, y_{2}\right)] the second point *[Tex \LARGE \left(-2,5\right)].



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



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



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



{{{m=(8)/(-4)}}} Subtract {{{2}}} from {{{-2}}} to get {{{-4}}}



{{{m=-2}}} Reduce



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