Question 403332
# 1




First let's find the slope of the line through the points *[Tex \LARGE \left(1,8\right)] and *[Tex \LARGE \left(-1,-20\right)]



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



{{{m=(-20-8)/(-1-1)}}} Plug in {{{y[2]=-20}}}, {{{y[1]=8}}}, {{{x[2]=-1}}}, and {{{x[1]=1}}}



{{{m=(-28)/(-1-1)}}} Subtract {{{8}}} from {{{-20}}} to get {{{-28}}}



{{{m=(-28)/(-2)}}} Subtract {{{1}}} from {{{-1}}} to get {{{-2}}}



{{{m=14}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(1,8\right)] and *[Tex \LARGE \left(-1,-20\right)] is {{{m=14}}}



Now let's use the point slope formula:



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



{{{y-8=14(x-1)}}} Plug in {{{m=14}}}, {{{x[1]=1}}}, and {{{y[1]=8}}}



{{{y-8=14x+14(-1)}}} Distribute



{{{y-8=14x-14}}} Multiply



{{{y=14x-14+8}}} Add 8 to both sides. 



{{{y=14x-6}}} Combine like terms. 




So the equation that goes through the points *[Tex \LARGE \left(1,8\right)] and *[Tex \LARGE \left(-1,-20\right)] is {{{y=14x-6}}}



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# 2




First let's find the slope of the line through the points *[Tex \LARGE \left(2,-1\right)] and *[Tex \LARGE \left(3,5\right)]



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



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



{{{m=(6)/(3-2)}}} Subtract {{{-1}}} from {{{5}}} to get {{{6}}}



{{{m=(6)/(1)}}} Subtract {{{2}}} from {{{3}}} to get {{{1}}}



{{{m=6}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(2,-1\right)] and *[Tex \LARGE \left(3,5\right)] is {{{m=6}}}



Now let's use the point slope formula:



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



{{{y--1=6(x-2)}}} Plug in {{{m=6}}}, {{{x[1]=2}}}, and {{{y[1]=-1}}}



{{{y+1=6(x-2)}}} Rewrite {{{y--1}}} as {{{y+1}}}



{{{y+1=6x+6(-2)}}} Distribute



{{{y+1=6x-12}}} Multiply



{{{y=6x-12-1}}} Subtract 1 from both sides. 



{{{y=6x-13}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(2,-1\right)] and *[Tex \LARGE \left(3,5\right)] is {{{y=6x-13}}}