Question 132977
Let's find the slope of the line through (3,4) and (4,2)





Let's denote the first point (3,4) as *[Tex \Large \left(x_{1},y_{1}\right)]. In other words, *[Tex \LARGE x_{1}=3] and *[Tex \LARGE y_{1}=4]


Now let's denote the second point (4,2) as *[Tex \Large \left(x_{2},y_{2}\right)]. In other words, *[Tex \Large x_{2}=4] 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=(2-4)/(4-3)}}} Plug in {{{y[2]=2}}},{{{y[1]=4}}},{{{x[2]=4}}},{{{x[1]=3}}}



{{{m=-2/1}}} Subtract the terms in the numerator {{{2-4}}} to get {{{-2}}}.  Subtract the terms in the denominator {{{4-3}}} to get {{{1}}}

  

{{{m=-2}}} Reduce


  

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Answer:


So the slope of the line through the points (3,4) and (4,2) is {{{m=-2}}}


So this line is parallel to the other line with a slope of -2