Question 602076


First let's find the slope of the line through the points *[Tex \LARGE \left(4,-2\right)] and *[Tex \LARGE \left(4,3\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(4,-2\right)]. So this means that {{{x[1]=4}}} and {{{y[1]=-2}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(4,3\right)].  So this means that {{{x[2]=4}}} and {{{y[2]=3}}}.



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



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



{{{m=(5)/(4-4)}}} Subtract {{{-2}}} from {{{3}}} to get {{{5}}}



{{{m=(5)/(0)}}} Subtract {{{4}}} from {{{4}}} to get {{{0}}}



Remember, you <b>cannot</b> divide by zero. So this means that the slope is undefined.



Since the slope is undefined, this means that the equation of the line through the points *[Tex \LARGE \left(4,-2\right)] and *[Tex \LARGE \left(4,3\right)] is {{{x=4}}} (this is a vertical line)