Question 309983

Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(5,4\right)]. So this means that {{{x[1]=5}}} and {{{y[1]=4}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(7,-10\right)].  So this means that {{{x[2]=7}}} and {{{y[2]=-10}}}.



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



{{{m=(-10-4)/(7-5)}}} Plug in {{{y[2]=-10}}}, {{{y[1]=4}}}, {{{x[2]=7}}}, and {{{x[1]=5}}}



{{{m=(-14)/(7-5)}}} Subtract {{{4}}} from {{{-10}}} to get {{{-14}}}



{{{m=(-14)/(2)}}} Subtract {{{5}}} from {{{7}}} to get {{{2}}}



{{{m=-7}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(5,4\right)] and *[Tex \LARGE \left(7,-10\right)] is {{{m=-7}}}