Question 395381


First let's find the slope of the line through the points *[Tex \LARGE \left(4,1\right)] and *[Tex \LARGE \left(12,7\right)]



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

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(12,7\right)].  So this means that {{{x[2]=12}}} and {{{y[2]=7}}}.



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



{{{m=(7-1)/(12-4)}}} Plug in {{{y[2]=7}}}, {{{y[1]=1}}}, {{{x[2]=12}}}, and {{{x[1]=4}}}



{{{m=(6)/(12-4)}}} Subtract {{{1}}} from {{{7}}} to get {{{6}}}



{{{m=(6)/(8)}}} Subtract {{{4}}} from {{{12}}} to get {{{8}}}



{{{m=3/4}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(4,1\right)] and *[Tex \LARGE \left(12,7\right)] is {{{m=3/4}}}



Now let's use the point slope formula:



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



{{{y-1=(3/4)(x-4)}}} Plug in {{{m=3/4}}}, {{{x[1]=4}}}, and {{{y[1]=1}}}



{{{y-1=(3/4)x+(3/4)(-4)}}} Distribute



{{{y-1=(3/4)x-3}}} Multiply



{{{y=(3/4)x-3+1}}} Add 1 to both sides. 



{{{y=(3/4)x-2}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(4,1\right)] and *[Tex \LARGE \left(12,7\right)] is {{{y=(3/4)x-2}}}



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