Question 540214

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



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(7,12\right)]. So this means that {{{x[1]=7}}} and {{{y[1]=12}}}.

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



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



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



{{{m=(-11)/(4-7)}}} Subtract {{{12}}} from {{{1}}} to get {{{-11}}}



{{{m=(-11)/(-3)}}} Subtract {{{7}}} from {{{4}}} to get {{{-3}}}



{{{m=11/3}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(7,12\right)] and *[Tex \LARGE \left(4,1\right)] is {{{m=11/3}}}



Now let's use the point slope formula:



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



{{{y-12=(11/3)(x-7)}}} Plug in {{{m=11/3}}}, {{{x[1]=7}}}, and {{{y[1]=12}}}



{{{y-12=(11/3)x+(11/3)(-7)}}} Distribute



{{{y-12=(11/3)x-77/3}}} Multiply



{{{y=(11/3)x-77/3+12}}} Add 12 to both sides. 



{{{y=(11/3)x-41/3}}} Combine like terms. note: If you need help with fractions, check out this <a href="http://www.algebra.com/algebra/homework/NumericFractions/fractions-solver.solver">solver</a>.



So the equation that goes through the points *[Tex \LARGE \left(7,12\right)] and *[Tex \LARGE \left(4,1\right)] is {{{y=(11/3)x-41/3}}}



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