Question 350960


First let's find the slope of the line through the points *[Tex \LARGE \left(9,2\right)] and *[Tex \LARGE \left(6,9\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(9,2\right)]. So this means that {{{x[1]=9}}} and {{{y[1]=2}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(6,9\right)].  So this means that {{{x[2]=6}}} and {{{y[2]=9}}}.



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



{{{m=(9-2)/(6-9)}}} Plug in {{{y[2]=9}}}, {{{y[1]=2}}}, {{{x[2]=6}}}, and {{{x[1]=9}}}



{{{m=(7)/(6-9)}}} Subtract {{{2}}} from {{{9}}} to get {{{7}}}



{{{m=(7)/(-3)}}} Subtract {{{9}}} from {{{6}}} to get {{{-3}}}



{{{m=-7/3}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(9,2\right)] and *[Tex \LARGE \left(6,9\right)] is {{{m=-7/3}}}



Now let's use the point slope formula:



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



{{{y-2=(-7/3)(x-9)}}} Plug in {{{m=-7/3}}}, {{{x[1]=9}}}, and {{{y[1]=2}}}



{{{y-2=(-7/3)x+(-7/3)(-9)}}} Distribute



{{{y-2=(-7/3)x+21}}} Multiply



{{{y=(-7/3)x+21+2}}} Add 2 to both sides. 



{{{y=(-7/3)x+23}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(9,2\right)] and *[Tex \LARGE \left(6,9\right)] is {{{y=(-7/3)x+23}}}



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