Question 207978
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(4,6\right)]. So this means that {{{x[1]=4}}} and {{{y[1]=6}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-3,5\right)].  So this means that {{{x[2]=-3}}} and {{{y[2]=5}}}.



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



{{{m=(5-6)/(-3-4)}}} Plug in {{{y[2]=5}}}, {{{y[1]=6}}}, {{{x[2]=-3}}}, and {{{x[1]=4}}}



{{{m=(-1)/(-3-4)}}} Subtract {{{6}}} from {{{5}}} to get {{{-1}}}



{{{m=(-1)/(-7)}}} Subtract {{{4}}} from {{{-3}}} to get {{{-7}}}



{{{m=1/7}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(4,6\right)] and *[Tex \LARGE \left(-3,5\right)] is {{{m=1/7}}}