Question 554904


First let's find the slope of the line through the points *[Tex \LARGE \left(4,2\right)] and *[Tex \LARGE \left(-6,7\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(4,2\right)]. So this means that {{{x[1]=4}}} and {{{y[1]=2}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-6,7\right)].  So this means that {{{x[2]=-6}}} and {{{y[2]=7}}}.



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



{{{m=(7-2)/(-6-4)}}} Plug in {{{y[2]=7}}}, {{{y[1]=2}}}, {{{x[2]=-6}}}, and {{{x[1]=4}}}



{{{m=(5)/(-6-4)}}} Subtract {{{2}}} from {{{7}}} to get {{{5}}}



{{{m=(5)/(-10)}}} Subtract {{{4}}} from {{{-6}}} to get {{{-10}}}



{{{m=-1/2}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(4,2\right)] and *[Tex \LARGE \left(-6,7\right)] is {{{m=-1/2}}}



Now let's use the point slope formula:



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



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



{{{y-2=(-1/2)x+(-1/2)(-4)}}} Distribute



{{{y-2=(-1/2)x+2}}} Multiply



{{{y=(-1/2)x+2+2}}} Add 2 to both sides. 



{{{y=(-1/2)x+4}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(4,2\right)] and *[Tex \LARGE \left(-6,7\right)] is {{{y=(-1/2)x+4}}}



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