Question 266311


First let's find the slope of the line through the points *[Tex \LARGE \left(3,-2\right)] and *[Tex \LARGE \left(3,6\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(3,-2\right)]. So this means that {{{x[1]=3}}} and {{{y[1]=-2}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(3,6\right)].  So this means that {{{x[2]=3}}} and {{{y[2]=6}}}.



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



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



{{{m=(8)/(3-3)}}} Subtract {{{-2}}} from {{{6}}} to get {{{8}}}



{{{m=(8)/(0)}}} Subtract {{{3}}} from {{{3}}} 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(3,-2\right)] and *[Tex \LARGE \left(3,6\right)] is {{{x=3}}}.