Question 567773


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



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

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(1,3\right)].  So this means that {{{x[2]=1}}} and {{{y[2]=3}}}.



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



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



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



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



{{{m=-2/3}}} Reduce



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



Now let's use the point slope formula:



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



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



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



{{{y-1=(-2/3)x+8/3}}} Multiply



{{{y=(-2/3)x+8/3+1}}} Add 1 to both sides. 



{{{y=(-2/3)x+11/3}}} 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(4,1\right)] and *[Tex \LARGE \left(1,3\right)] is {{{y=(-2/3)x+11/3}}}