Question 712226

First let's find the slope of the line through the points *[Tex \LARGE \left(5,0\right)] and *[Tex \LARGE \left(-8,-3\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(5,0\right)]. So this means that {{{x[1]=5}}} and {{{y[1]=0}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-8,-3\right)].  So this means that {{{x[2]=-8}}} and {{{y[2]=-3}}}.



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



{{{m=(-3-0)/(-8-5)}}} Plug in {{{y[2]=-3}}}, {{{y[1]=0}}}, {{{x[2]=-8}}}, and {{{x[1]=5}}}



{{{m=(-3)/(-8-5)}}} Subtract {{{0}}} from {{{-3}}} to get {{{-3}}}



{{{m=(-3)/(-13)}}} Subtract {{{5}}} from {{{-8}}} to get {{{-13}}}



{{{m=3/13}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(5,0\right)] and *[Tex \LARGE \left(-8,-3\right)] is {{{m=3/13}}}



Now let's use the point slope formula:



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



{{{y-0=(3/13)(x-5)}}} Plug in {{{m=3/13}}}, {{{x[1]=5}}}, and {{{y[1]=0}}}



{{{y-0=(3/13)x+(3/13)(-5)}}} Distribute



{{{y-0=(3/13)x-15/13}}} Multiply



{{{y=(3/13)x-15/13}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(5,0\right)] and *[Tex \LARGE \left(-8,-3\right)] is {{{y=(3/13)x-15/13}}}