Question 701788


First let's find the slope of the line through the points *[Tex \LARGE \left(-1,5\right)] and *[Tex \LARGE \left(2,-4\right)]



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

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



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



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



{{{m=(-9)/(2--1)}}} Subtract {{{5}}} from {{{-4}}} to get {{{-9}}}



{{{m=(-9)/(3)}}} Subtract {{{-1}}} from {{{2}}} to get {{{3}}}



{{{m=-3}}} Reduce



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



{{{y-5=-3(x+1)}}} Rewrite {{{x--1}}} as {{{x+1}}}



{{{y-5=-3x+-3(1)}}} Distribute



{{{y-5=-3x-3}}} Multiply



{{{y=-3x-3+5}}} Add 5 to both sides. 



{{{y=-3x+2}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(-1,5\right)] and *[Tex \LARGE \left(2,-4\right)] is {{{y=-3x+2}}}