Question 536148


First let's find the slope of the line through the points *[Tex \LARGE \left(-5,-4\right)] and *[Tex \LARGE \left(7,-5\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-5,-4\right)]. So this means that {{{x[1]=-5}}} and {{{y[1]=-4}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(7,-5\right)].  So this means that {{{x[2]=7}}} and {{{y[2]=-5}}}.



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



{{{m=(-5--4)/(7--5)}}} Plug in {{{y[2]=-5}}}, {{{y[1]=-4}}}, {{{x[2]=7}}}, and {{{x[1]=-5}}}



{{{m=(-1)/(7--5)}}} Subtract {{{-4}}} from {{{-5}}} to get {{{-1}}}



{{{m=(-1)/(12)}}} Subtract {{{-5}}} from {{{7}}} to get {{{12}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(-5,-4\right)] and *[Tex \LARGE \left(7,-5\right)] is {{{m=-1/12}}}



Now let's use the point slope formula:



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



{{{y--4=(-1/12)(x--5)}}} Plug in {{{m=-1/12}}}, {{{x[1]=-5}}}, and {{{y[1]=-4}}}



{{{y--4=(-1/12)(x+5)}}} Rewrite {{{x--5}}} as {{{x+5}}}



{{{y+4=(-1/12)(x+5)}}} Rewrite {{{y--4}}} as {{{y+4}}}



So the equation that goes through the points *[Tex \LARGE \left(-5,-4\right)] and *[Tex \LARGE \left(7,-5\right)] in point slope form is {{{y+4=(-1/12)(x+5)}}}



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