Question 626708


First let's find the slope of the line through the points *[Tex \LARGE \left(-3,-5\right)] and *[Tex \LARGE \left(-2,-3\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-3,-5\right)]. So this means that {{{x[1]=-3}}} and {{{y[1]=-5}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-2,-3\right)].  So this means that {{{x[2]=-2}}} and {{{y[2]=-3}}}.



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



{{{m=(-3--5)/(-2--3)}}} Plug in {{{y[2]=-3}}}, {{{y[1]=-5}}}, {{{x[2]=-2}}}, and {{{x[1]=-3}}}



{{{m=(2)/(-2--3)}}} Subtract {{{-5}}} from {{{-3}}} to get {{{2}}}



{{{m=(2)/(1)}}} Subtract {{{-3}}} from {{{-2}}} to get {{{1}}}



{{{m=2}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(-3,-5\right)] and *[Tex \LARGE \left(-2,-3\right)] is {{{m=2}}}



Now let's use the point slope formula:



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



{{{y--5=2(x--3)}}} Plug in {{{m=2}}}, {{{x[1]=-3}}}, and {{{y[1]=-5}}}



{{{y--5=2(x+3)}}} Rewrite {{{x--3}}} as {{{x+3}}}



{{{y+5=2(x+3)}}} Rewrite {{{y--5}}} as {{{y+5}}}



{{{y+5=2x+2(3)}}} Distribute



{{{y+5=2x+6}}} Multiply



{{{y=2x+6-5}}} Subtract 5 from both sides. 



{{{y=2x+1}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(-3,-5\right)] and *[Tex \LARGE \left(-2,-3\right)] is {{{y=2x+1}}}



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