Question 254613
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(7,2\right)]. So this means that {{{x[1]=7}}} and {{{y[1]=2}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(10,-4\right)].  So this means that {{{x[2]=10}}} and {{{y[2]=-4}}}.



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



{{{m=(-4-2)/(10-7)}}} Plug in {{{y[2]=-4}}}, {{{y[1]=2}}}, {{{x[2]=10}}}, and {{{x[1]=7}}}



{{{m=(-6)/(10-7)}}} Subtract {{{2}}} from {{{-4}}} to get {{{-6}}}



{{{m=(-6)/(3)}}} Subtract {{{7}}} from {{{10}}} to get {{{3}}}



{{{m=-2}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(7,2\right)] and *[Tex \LARGE \left(10,-4\right)] is {{{m=-2}}}