Question 509002


First let's find the slope of the line through the points *[Tex \LARGE \left(-6,-4\right)] and *[Tex \LARGE \left(2,-5\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-6,-4\right)]. So this means that {{{x[1]=-6}}} and {{{y[1]=-4}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(2,-5\right)].  So this means that {{{x[2]=2}}} and {{{y[2]=-5}}}.



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



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



{{{m=(-1)/(2--6)}}} Subtract {{{-4}}} from {{{-5}}} to get {{{-1}}}



{{{m=(-1)/(8)}}} Subtract {{{-6}}} from {{{2}}} to get {{{8}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(-6,-4\right)] and *[Tex \LARGE \left(2,-5\right)] is {{{m=-1/8}}}



Now let's use the point slope formula:



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



{{{y--4=(-1/8)(x--6)}}} Plug in {{{m=-1/8}}}, {{{x[1]=-6}}}, and {{{y[1]=-4}}}



{{{y--4=(-1/8)(x+6)}}} Rewrite {{{x--6}}} as {{{x+6}}}



{{{y+4=(-1/8)(x+6)}}} Rewrite {{{y--4}}} as {{{y+4}}}



{{{y+4=(-1/8)x+(-1/8)(6)}}} Distribute



{{{y+4=(-1/8)x-3/4}}} Multiply



{{{y=(-1/8)x-3/4-4}}} Subtract 4 from both sides. 



{{{y=(-1/8)x-19/4}}} 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(-6,-4\right)] and *[Tex \LARGE \left(2,-5\right)] is {{{y=(-1/8)x-19/4}}}