Question 128493
I'll do the first two to get you started



# 1





Let's denote the first point (4,2) as *[Tex \Large \left(x_{1},y_{1}\right)]. In other words, *[Tex \LARGE x_{1}=4] and *[Tex \LARGE y_{1}=2]


Now let's denote the second point (7,8) as *[Tex \Large \left(x_{2},y_{2}\right)]. In other words, *[Tex \Large x_{2}=7] and *[Tex \Large y_{2}=8]




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


{{{m=(8-2)/(7-4)}}} Plug in {{{y[2]=8}}},{{{y[1]=2}}},{{{x[2]=7}}},{{{x[1]=4}}}



{{{m=6/3}}} Subtract the terms in the numerator {{{8-2}}} to get {{{6}}}.  Subtract the terms in the denominator {{{7-4}}} to get {{{3}}}

  

{{{m=2}}} Reduce


  

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Answer:


So the slope of the line through the points (4,2) and (7,8) is {{{m=2}}}





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# 2





Let's denote the first point (-7,-9) as *[Tex \Large \left(x_{1},y_{1}\right)]. In other words, *[Tex \LARGE x_{1}=-7] and *[Tex \LARGE y_{1}=-9]


Now let's denote the second point (3,-2) as *[Tex \Large \left(x_{2},y_{2}\right)]. In other words, *[Tex \Large x_{2}=3] and *[Tex \Large y_{2}=-2]




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


{{{m=(-2--9)/(3--7)}}} Plug in {{{y[2]=-2}}},{{{y[1]=-9}}},{{{x[2]=3}}},{{{x[1]=-7}}}



{{{m=7/10}}} Subtract the terms in the numerator {{{-2--9}}} to get {{{7}}}.  Subtract the terms in the denominator {{{3--7}}} to get {{{10}}}

  

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Answer:


So the slope of the line through the points (-7,-9) and (3,-2) is {{{m=7/10}}}