Question 553253


First let's find the slope of the line through the points *[Tex \LARGE \left(3,7\right)] and *[Tex \LARGE \left(-1,5\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(3,7\right)]. So this means that {{{x[1]=3}}} and {{{y[1]=7}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-1,5\right)].  So this means that {{{x[2]=-1}}} and {{{y[2]=5}}}.



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



{{{m=(5-7)/(-1-3)}}} Plug in {{{y[2]=5}}}, {{{y[1]=7}}}, {{{x[2]=-1}}}, and {{{x[1]=3}}}



{{{m=(-2)/(-1-3)}}} Subtract {{{7}}} from {{{5}}} to get {{{-2}}}



{{{m=(-2)/(-4)}}} Subtract {{{3}}} from {{{-1}}} to get {{{-4}}}



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



So the slope of the line that goes through the points *[Tex \LARGE \left(3,7\right)] and *[Tex \LARGE \left(-1,5\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-7=(1/2)(x-3)}}} Plug in {{{m=1/2}}}, {{{x[1]=3}}}, and {{{y[1]=7}}}



{{{y-7=(1/2)x+(1/2)(-3)}}} Distribute



{{{y-7=(1/2)x-3/2}}} Multiply



{{{y=(1/2)x-3/2+7}}} Add 7 to both sides. 



{{{y=(1/2)x+11/2}}} 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(3,7\right)] and *[Tex \LARGE \left(-1,5\right)] is {{{y=(1/2)x+11/2}}}



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