Question 588315
First let's find the slope of the line through the points *[Tex \LARGE \left(-1,3\right)] and *[Tex \LARGE \left(3,-9\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-1,3\right)]. So this means that {{{x[1]=-1}}} and {{{y[1]=3}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(3,-9\right)].  So this means that {{{x[2]=3}}} and {{{y[2]=-9}}}.



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



{{{m=(-9-3)/(3--1)}}} Plug in {{{y[2]=-9}}}, {{{y[1]=3}}}, {{{x[2]=3}}}, and {{{x[1]=-1}}}



{{{m=(-12)/(3--1)}}} Subtract {{{3}}} from {{{-9}}} to get {{{-12}}}



{{{m=(-12)/(4)}}} Subtract {{{-1}}} from {{{3}}} to get {{{4}}}



{{{m=-3}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-1,3\right)] and *[Tex \LARGE \left(3,-9\right)] is {{{m=-3}}}



Now let's use the point slope formula:



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



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



{{{y-3=-3(x+1)}}} Rewrite {{{x--1}}} as {{{x+1}}}



So the answer is {{{y-3=-3(x+1)}}}


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