Question 375059


First let's find the slope of the line through the points *[Tex \LARGE \left(9,136\right)] and *[Tex \LARGE \left(3,40\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(9,136\right)]. So this means that {{{x[1]=9}}} and {{{y[1]=136}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(3,40\right)].  So this means that {{{x[2]=3}}} and {{{y[2]=40}}}.



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



{{{m=(40-136)/(3-9)}}} Plug in {{{y[2]=40}}}, {{{y[1]=136}}}, {{{x[2]=3}}}, and {{{x[1]=9}}}



{{{m=(-96)/(3-9)}}} Subtract {{{136}}} from {{{40}}} to get {{{-96}}}



{{{m=(-96)/(-6)}}} Subtract {{{9}}} from {{{3}}} to get {{{-6}}}



{{{m=16}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(9,136\right)] and *[Tex \LARGE \left(3,40\right)] is {{{m=16}}}



Now let's use the point slope formula:



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



{{{y-136=16(x-9)}}} Plug in {{{m=16}}}, {{{x[1]=9}}}, and {{{y[1]=136}}}



{{{y-136=16x+16(-9)}}} Distribute



{{{y-136=16x-144}}} Multiply



{{{y=16x-144+136}}} Add 136 to both sides. 



{{{y=16x-8}}} Combine like terms. 



{{{y=16x-8}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(9,136\right)] and *[Tex \LARGE \left(3,40\right)] is {{{y=16x-8}}}



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