Question 173073

First let's find the slope of the line through the points *[Tex \LARGE \left(5,9\right)] and *[Tex \LARGE \left(1,-23\right)]



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



{{{m=(-23-9)/(1-5)}}} Plug in {{{y[2]=-23}}}, {{{y[1]=9}}}, {{{x[2]=1}}}, and {{{x[1]=5}}}



{{{m=(-32)/(1-5)}}} Subtract {{{9}}} from {{{-23}}} to get {{{-32}}}



{{{m=(-32)/(-4)}}} Subtract {{{5}}} from {{{1}}} to get {{{-4}}}



{{{m=8}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(5,9\right)] and *[Tex \LARGE \left(1,-23\right)] is {{{m=8}}}



Now let's use the point slope formula:



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



{{{y-9=8(x-5)}}} Plug in {{{m=8}}}, {{{x[1]=5}}}, and {{{y[1]=9}}}



{{{y-9=8x+8(-5)}}} Distribute



{{{y-9=8x-40}}} Multiply



{{{y=8x-40+9}}} Add 9 to both sides. 



{{{y=8x-31}}} Combine like terms. 



{{{y=8x-31}}} Simplify



So the equation that goes through the points *[Tex \LARGE \left(5,9\right)] and *[Tex \LARGE \left(1,-23\right)] is {{{y=8x-31}}}