Question 170562

First let's find the slope of the line through the points *[Tex \LARGE \left(5,2\right)] and *[Tex \LARGE \left(-7,3\right)]



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



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



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



{{{m=(1)/(-12)}}} Subtract {{{5}}} from {{{-7}}} to get {{{-12}}}



{{{m=-1/12}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(5,2\right)] and *[Tex \LARGE \left(-7,3\right)] is {{{m=-1/12}}}



Now let's use the point slope formula:



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



{{{y-2=(-1/12)(x-5)}}} Plug in {{{m=-1/12}}}, {{{x[1]=5}}}, and {{{y[1]=2}}}



{{{y-2=(-1/12)x+(-1/12)(-5)}}} Distribute



{{{y-2=(-1/12)x+5/12}}} Multiply



{{{y=(-1/12)x+5/12+2}}} Add 2 to both sides. 



{{{y=(-1/12)x+29/12}}} 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=(-1/12)x+29/12}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(5,2\right)] and *[Tex \LARGE \left(-7,3\right)] is {{{y=(-1/12)x+29/12}}}