Question 456691
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(2,-14\right)]. So this means that {{{x[1]=2}}} and {{{y[1]=-14}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-7,4\right)].  So this means that {{{x[2]=-7}}} and {{{y[2]=4}}}.



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



{{{m=(4--14)/(-7-2)}}} Plug in {{{y[2]=4}}}, {{{y[1]=-14}}}, {{{x[2]=-7}}}, and {{{x[1]=2}}}



{{{m=(18)/(-7-2)}}} Subtract {{{-14}}} from {{{4}}} to get {{{18}}}



{{{m=(18)/(-9)}}} Subtract {{{2}}} from {{{-7}}} to get {{{-9}}}



{{{m=-2}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(2,-14\right)] and *[Tex \LARGE \left(-7,4\right)] is {{{m=-2}}}