Question 339956


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



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



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



{{{m=(10)/(-1-5)}}} Subtract {{{-7}}} from {{{3}}} to get {{{10}}}



{{{m=(10)/(-6)}}} Subtract {{{5}}} from {{{-1}}} to get {{{-6}}}



{{{m=-5/3}}} Reduce



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



Now let's use the point slope formula:



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



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



{{{y+7=(-5/3)(x-5)}}} Rewrite {{{y--7}}} as {{{y+7}}}



{{{y+7=(-5/3)x+(-5/3)(-5)}}} Distribute



{{{y+7=(-5/3)x+25/3}}} Multiply



{{{y=(-5/3)x+25/3-7}}} Subtract 7 from both sides. 



{{{y=(-5/3)x+4/3}}} 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>.



{{{y=(-5/3)x+4/3}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(5,-7\right)] and *[Tex \LARGE \left(-1,3\right)] is {{{y=(-5/3)x+4/3}}}


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