Question 594140
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(2,5\right)]. So this means that {{{x[1]=2}}} and {{{y[1]=5}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-3,4\right)].  So this means that {{{x[2]=-3}}} and {{{y[2]=4}}}.



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



{{{m=(4-5)/(-3-2)}}} Plug in {{{y[2]=4}}}, {{{y[1]=5}}}, {{{x[2]=-3}}}, and {{{x[1]=2}}}



{{{m=(-1)/(-3-2)}}} Subtract {{{5}}} from {{{4}}} to get {{{-1}}}



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



{{{m=1/5}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(2,5\right)] and *[Tex \LARGE \left(-3,4\right)] is {{{m=1/5}}}