Question 738366


First let's find the slope of the line through the points *[Tex \LARGE \left(5,7\right)] and *[Tex \LARGE \left(5,-7\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(5,7\right)]. So this means that {{{x[1]=5}}} and {{{y[1]=7}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(5,-7\right)].  So this means that {{{x[2]=5}}} and {{{y[2]=-7}}}.



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



{{{m=(-7-7)/(5-5)}}} Plug in {{{y[2]=-7}}}, {{{y[1]=7}}}, {{{x[2]=5}}}, and {{{x[1]=5}}}



{{{m=(-14)/(5-5)}}} Subtract {{{7}}} from {{{-7}}} to get {{{-14}}}



{{{m=(-14)/(0)}}} Subtract {{{5}}} from {{{5}}} 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(5,7\right)] and *[Tex \LARGE \left(5,-7\right)] is {{{x=5}}}.