Question 627679
First let's find the slope of the line through the points *[Tex \LARGE \left(7,-1\right)] and *[Tex \LARGE \left(6,5\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(7,-1\right)]. So this means that {{{x[1]=7}}} and {{{y[1]=-1}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(6,5\right)].  So this means that {{{x[2]=6}}} and {{{y[2]=5}}}.



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



{{{m=(5--1)/(6-7)}}} Plug in {{{y[2]=5}}}, {{{y[1]=-1}}}, {{{x[2]=6}}}, and {{{x[1]=7}}}



{{{m=(6)/(6-7)}}} Subtract {{{-1}}} from {{{5}}} to get {{{6}}}



{{{m=(6)/(-1)}}} Subtract {{{7}}} from {{{6}}} to get {{{-1}}}



{{{m=-6}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(7,-1\right)] and *[Tex \LARGE \left(6,5\right)] is {{{m=-6}}}



Now let's use the point slope formula:



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



{{{y--1=-6(x-7)}}} Plug in {{{m=-6}}}, {{{x[1]=7}}}, and {{{y[1]=-1}}}



{{{y+1=-6(x-7)}}} Rewrite {{{y--1}}} as {{{y+1}}}



{{{y+1=-6x+-6(-7)}}} Distribute



{{{y+1=-6x+42}}} Multiply



{{{y=-6x+42-1}}} Subtract 1 from both sides. 



{{{y=-6x+41}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(7,-1\right)] and *[Tex \LARGE \left(6,5\right)] is {{{y=-6x+41}}}


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