Question 654629
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(-1,-5\right)].  So this means that {{{x[2]=-1}}} and {{{y[2]=-5}}}.



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



{{{m=(-5--2)/(-1-7)}}} Plug in {{{y[2]=-5}}}, {{{y[1]=-2}}}, {{{x[2]=-1}}}, and {{{x[1]=7}}}



{{{m=(-3)/(-1-7)}}} Subtract {{{-2}}} from {{{-5}}} to get {{{-3}}}



{{{m=(-3)/(-8)}}} Subtract {{{7}}} from {{{-1}}} to get {{{-8}}}



{{{m=3/8}}} Reduce


So the slope of the line that goes through the points *[Tex \LARGE \left(7,-2\right)] and *[Tex \LARGE \left(-1,-5\right)] is {{{m=3/8}}}