Question 320576


First let's find the slope of the line through the points *[Tex \LARGE \left(4,0\right)] and *[Tex \LARGE \left(-8,5\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(4,0\right)]. So this means that {{{x[1]=4}}} and {{{y[1]=0}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-8,5\right)].  So this means that {{{x[2]=-8}}} and {{{y[2]=5}}}.



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



{{{m=(5-0)/(-8-4)}}} Plug in {{{y[2]=5}}}, {{{y[1]=0}}}, {{{x[2]=-8}}}, and {{{x[1]=4}}}



{{{m=(5)/(-8-4)}}} Subtract {{{0}}} from {{{5}}} to get {{{5}}}



{{{m=(5)/(-12)}}} Subtract {{{4}}} from {{{-8}}} to get {{{-12}}}



{{{m=-5/12}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(4,0\right)] and *[Tex \LARGE \left(-8,5\right)] is {{{m=-5/12}}}



Now let's use the point slope formula:



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



{{{y-0=(-5/12)(x-4)}}} Plug in {{{m=-5/12}}}, {{{x[1]=4}}}, and {{{y[1]=0}}}



{{{y-0=(-5/12)x+(-5/12)(-4)}}} Distribute



{{{y-0=(-5/12)x+5/3}}} Multiply



{{{y=(-5/12)x+5/3}}} Simplify 



So the equation that goes through the points *[Tex \LARGE \left(4,0\right)] and *[Tex \LARGE \left(-8,5\right)] is {{{y=(-5/12)x+5/3}}}



I'll let you convert that equation into standard form.