Question 556313


First let's find the slope of the line through the points *[Tex \LARGE \left(2,-7\right)] and *[Tex \LARGE \left(5,-1\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(2,-7\right)]. So this means that {{{x[1]=2}}} and {{{y[1]=-7}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(5,-1\right)].  So this means that {{{x[2]=5}}} and {{{y[2]=-1}}}.



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



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



{{{m=(6)/(5-2)}}} Subtract {{{-7}}} from {{{-1}}} to get {{{6}}}



{{{m=(6)/(3)}}} Subtract {{{2}}} from {{{5}}} to get {{{3}}}



{{{m=2}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(2,-7\right)] and *[Tex \LARGE \left(5,-1\right)] is {{{m=2}}}



Now let's use the point slope formula:



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



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



{{{y+7=2(x-2)}}} Rewrite {{{y--7}}} as {{{y+7}}}



{{{y+7=2x+2(-2)}}} Distribute



{{{y+7=2x-4}}} Multiply



{{{y=2x-4-7}}} Subtract 7 from both sides. 



{{{y=2x-11}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(2,-7\right)] and *[Tex \LARGE \left(5,-1\right)] is {{{y=2x-11}}}


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