Question 571184


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



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

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



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



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



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



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



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



Now let's use the point slope formula:



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



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



{{{y-1=(-3/5)(x+3)}}} Rewrite {{{x--3}}} as {{{x+3}}}



{{{y-1=(-3/5)x+(-3/5)(3)}}} Distribute



{{{y-1=(-3/5)x-9/5}}} Multiply



{{{y=(-3/5)x-9/5+1}}} Add 1 to both sides. 



{{{y=(-3/5)x-4/5}}} 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(-3,1\right)] and *[Tex \LARGE \left(2,-2\right)] is {{{y=(-3/5)x-4/5}}}