Question 552747

First let's find the slope of the line through the points *[Tex \LARGE \left(-7,-6\right)] and *[Tex \LARGE \left(-1,-5\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-7,-6\right)]. So this means that {{{x[1]=-7}}} and {{{y[1]=-6}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-1,-5\right)].  So this means that {{{x[2]=-1}}} and {{{y[2]=-5}}}.



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



{{{m=(-5--6)/(-1--7)}}} Plug in {{{y[2]=-5}}}, {{{y[1]=-6}}}, {{{x[2]=-1}}}, and {{{x[1]=-7}}}



{{{m=(1)/(-1--7)}}} Subtract {{{-6}}} from {{{-5}}} to get {{{1}}}



{{{m=(1)/(6)}}} Subtract {{{-7}}} from {{{-1}}} to get {{{6}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(-7,-6\right)] and *[Tex \LARGE \left(-1,-5\right)] is {{{m=1/6}}}



Now let's use the point slope formula:



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



{{{y--6=(1/6)(x--7)}}} Plug in {{{m=1/6}}}, {{{x[1]=-7}}}, and {{{y[1]=-6}}}



{{{y--6=(1/6)(x+7)}}} Rewrite {{{x--7}}} as {{{x+7}}}



{{{y+6=(1/6)(x+7)}}} Rewrite {{{y--6}}} as {{{y+6}}}



{{{y+6=(1/6)x+(1/6)(7)}}} Distribute



{{{y+6=(1/6)x+7/6}}} Multiply



{{{y=(1/6)x+7/6-6}}} Subtract 6 from both sides. 



{{{y=(1/6)x-29/6}}} 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(-7,-6\right)] and *[Tex \LARGE \left(-1,-5\right)] is {{{y=(1/6)x-29/6}}}



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