Question 339900


First let's find the slope of the line through the points *[Tex \LARGE \left(4,2\right)] and *[Tex \LARGE \left(1,3\right)]



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



{{{m=(3-2)/(1-4)}}} Plug in {{{y[2]=3}}}, {{{y[1]=2}}}, {{{x[2]=1}}}, and {{{x[1]=4}}}



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



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



{{{m=-1/3}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(4,2\right)] and *[Tex \LARGE \left(1,3\right)] is {{{m=-1/3}}}



Now let's use the point slope formula:



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



{{{y-2=(-1/3)(x-4)}}} Plug in {{{m=-1/3}}}, {{{x[1]=4}}}, and {{{y[1]=2}}}



{{{y-2=(-1/3)x+(-1/3)(-4)}}} Distribute



{{{y-2=(-1/3)x+4/3}}} Multiply



{{{y=(-1/3)x+4/3+2}}} Add 2 to both sides. 



{{{y=(-1/3)x+10/3}}} 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=(-1/3)x+10/3}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(4,2\right)] and *[Tex \LARGE \left(1,3\right)] is {{{y=(-1/3)x+10/3}}}



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