Question 847706


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



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

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



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



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



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



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



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



Now let's use the point slope formula:



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



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



{{{y+1=(3/2)(x-1)}}} Rewrite {{{y--1}}} as {{{y+1}}}



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



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



{{{y=(3/2)x-3/2-1}}} Subtract 1 from both sides. 



{{{y=(3/2)x-5/2}}} 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,-1\right)] and *[Tex \LARGE \left(3,2\right)] is {{{y=(3/2)x-5/2}}}