Question 545347


First let's find the slope of the line through the points *[Tex \LARGE \left(-5,-1\right)] and *[Tex \LARGE \left(6,-4\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-5,-1\right)]. So this means that {{{x[1]=-5}}} and {{{y[1]=-1}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(6,-4\right)].  So this means that {{{x[2]=6}}} and {{{y[2]=-4}}}.



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



{{{m=(-4--1)/(6--5)}}} Plug in {{{y[2]=-4}}}, {{{y[1]=-1}}}, {{{x[2]=6}}}, and {{{x[1]=-5}}}



{{{m=(-3)/(6--5)}}} Subtract {{{-1}}} from {{{-4}}} to get {{{-3}}}



{{{m=(-3)/(11)}}} Subtract {{{-5}}} from {{{6}}} to get {{{11}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(-5,-1\right)] and *[Tex \LARGE \left(6,-4\right)] is {{{m=-3/11}}}



Now let's use the point slope formula:



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



{{{y--1=(-3/11)(x--5)}}} Plug in {{{m=-3/11}}}, {{{x[1]=-5}}}, and {{{y[1]=-1}}}



{{{y--1=(-3/11)(x+5)}}} Rewrite {{{x--5}}} as {{{x+5}}}



{{{y+1=(-3/11)(x+5)}}} Rewrite {{{y--1}}} as {{{y+1}}}



{{{y+1=(-3/11)x+(-3/11)(5)}}} Distribute



{{{y+1=(-3/11)x-15/11}}} Multiply



{{{y=(-3/11)x-15/11-1}}} Subtract 1 from both sides. 



{{{y=(-3/11)x-26/11}}} 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(-5,-1\right)] and *[Tex \LARGE \left(6,-4\right)] is {{{y=(-3/11)x-26/11}}}