Question 604063


First let's find the slope of the line through the points *[Tex \LARGE \left(-13,22\right)] and *[Tex \LARGE \left(8,-17\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-13,22\right)]. So this means that {{{x[1]=-13}}} and {{{y[1]=22}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(8,-17\right)].  So this means that {{{x[2]=8}}} and {{{y[2]=-17}}}.



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



{{{m=(-17-22)/(8--13)}}} Plug in {{{y[2]=-17}}}, {{{y[1]=22}}}, {{{x[2]=8}}}, and {{{x[1]=-13}}}



{{{m=(-39)/(8--13)}}} Subtract {{{22}}} from {{{-17}}} to get {{{-39}}}



{{{m=(-39)/(21)}}} Subtract {{{-13}}} from {{{8}}} to get {{{21}}}



{{{m=-13/7}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-13,22\right)] and *[Tex \LARGE \left(8,-17\right)] is {{{m=-13/7}}}



Now let's use the point slope formula:



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



{{{y-22=(-13/7)(x--13)}}} Plug in {{{m=-13/7}}}, {{{x[1]=-13}}}, and {{{y[1]=22}}}



{{{y-22=(-13/7)(x+13)}}} Rewrite {{{x--13}}} as {{{x+13}}}



{{{y-22=(-13/7)x+(-13/7)(13)}}} Distribute



{{{y-22=(-13/7)x-169/7}}} Multiply



{{{y=(-13/7)x-169/7+22}}} Add 22 to both sides. 



{{{y=(-13/7)x-15/7}}} 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(-13,22\right)] and *[Tex \LARGE \left(8,-17\right)] is {{{y=(-13/7)x-15/7}}}