Question 199529
# 1

Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-4,1\right)] and *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(3,5\right)].



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



{{{m=(5-1)/(3--4)}}} Plug in {{{y[2]=5}}}, {{{y[1]=1}}}, {{{x[2]=3}}}, and {{{x[1]=-4}}}



{{{m=(4)/(3--4)}}} Subtract {{{1}}} from {{{5}}} to get {{{4}}}



{{{m=(4)/(7)}}} Subtract {{{-4}}} from {{{3}}} to get {{{7}}}



So the slope of the line that goes through the points *[Tex \LARGE \left(-4,1\right)] and *[Tex \LARGE \left(3,5\right)] is {{{m=4/7}}}



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# 2




First let's find the slope of the line through the points *[Tex \LARGE \left(4,6\right)] and *[Tex \LARGE \left(-7,-3\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(4,6\right)] and *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-7,-3\right)].



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



{{{m=(-3-6)/(-7-4)}}} Plug in {{{y[2]=-3}}}, {{{y[1]=6}}}, {{{x[2]=-7}}}, and {{{x[1]=4}}}



{{{m=(-9)/(-7-4)}}} Subtract {{{6}}} from {{{-3}}} to get {{{-9}}}



{{{m=(-9)/(-11)}}} Subtract {{{4}}} from {{{-7}}} to get {{{-11}}}



{{{m=9/11}}} Reduce



So the slope of the line that goes through the points *[Tex \LARGE \left(4,6\right)] and *[Tex \LARGE \left(-7,-3\right)] is {{{m=9/11}}}



Now let's use the point slope formula:



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



{{{y-6=(9/11)(x-4)}}} Plug in {{{m=9/11}}}, {{{x[1]=4}}}, and {{{y[1]=6}}}



{{{y-6=(9/11)x+(9/11)(-4)}}} Distribute



{{{y-6=(9/11)x-36/11}}} Multiply



{{{y=(9/11)x-36/11+6}}} Add 6 to both sides. 



{{{y=(9/11)x+30/11}}} Combine like terms. 



So the equation that goes through the points *[Tex \LARGE \left(4,6\right)] and *[Tex \LARGE \left(-7,-3\right)] is {{{y=(9/11)x+30/11}}}