Question 636408
First let's find the slope of the line through the points *[Tex \LARGE \left(1,-3\right)] and *[Tex \LARGE \left(4,-2\right)]



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

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(4,-2\right)].  So this means that {{{x[2]=4}}} and {{{y[2]=-2}}}.



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



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



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



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



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



{{{y+3=(1/3)(x-1)}}} Rewrite {{{y--3}}} as {{{y+3}}}



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



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



{{{y=(1/3)x-1/3-3}}} Subtract 3 from 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>.



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