Question 146192

First let's find the slope through the points *[Tex \LARGE \left(7.5,2\right)] and *[Tex \LARGE \left(7.5,9\right)]



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



{{{m=(9-2)/(7.5-7.5)}}} Plug in {{{y[2]=9}}}, {{{y[1]=2}}}, {{{x[2]=7.5}}}, {{{x[1]=7.5}}},



{{{m=(7)/(7.5-7.5)}}} Subtract {{{2}}} from {{{9}}} to get {{{7}}}



{{{m=(7)/(0)}}} Subtract {{{7.5}}} from {{{7.5}}} 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(7.5,2\right)] and *[Tex \LARGE \left(7.5,9\right)] is {{{x=7.5}}}, which is simply a vertical line through {{{x=7.5}}}.