Question 318029
Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(0,2\right)]. So this means that {{{x[1]=0}}} and {{{y[1]=2}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-1,-2\right)].  So this means that {{{x[2]=-1}}} and {{{y[2]=-2}}}.



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



{{{m=(-2-2)/(-1-0)}}} Plug in {{{y[2]=-2}}}, {{{y[1]=2}}}, {{{x[2]=-1}}}, and {{{x[1]=0}}}



{{{m=(-4)/(-1-0)}}} Subtract {{{2}}} from {{{-2}}} to get {{{-4}}}



{{{m=(-4)/(-1)}}} Subtract {{{0}}} from {{{-1}}} to get {{{-1}}}



{{{m=4}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(0,2\right)] and *[Tex \LARGE \left(-1,-2\right)] is {{{m=4}}}