Question 577626

First let's find the slope of the line through the points *[Tex \LARGE \left(-6,-4\right)] and *[Tex \LARGE \left(6,-6\right)]



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

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(6,-6\right)].  So this means that {{{x[2]=6}}} and {{{y[2]=-6}}}.



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



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



{{{m=(-2)/(6--6)}}} Subtract {{{-4}}} from {{{-6}}} to get {{{-2}}}



{{{m=(-2)/(12)}}} Subtract {{{-6}}} from {{{6}}} to get {{{12}}}



{{{m=-1/6}}} Reduce



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



Now let's use the point slope formula:



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



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



{{{y--4=(-1/6)(x+6)}}} Rewrite {{{x--6}}} as {{{x+6}}}



{{{y+4=(-1/6)(x+6)}}} Rewrite {{{y--4}}} as {{{y+4}}}



{{{y+4=(-1/6)x+(-1/6)(6)}}} Distribute



{{{y+4=(-1/6)x-1}}} Multiply



{{{y=(-1/6)x-1-4}}} Subtract 4 from both sides. 



{{{y=(-1/6)x-5}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(-6,-4\right)] and *[Tex \LARGE \left(6,-6\right)] is {{{y=(-1/6)x-5}}}



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