Question 501950


First let's find the slope of the line through the points *[Tex \LARGE \left(-8,-5\right)] and *[Tex \LARGE \left(-8,-9\right)]



Note: *[Tex \LARGE \left(x_{1}, y_{1}\right)] is the first point *[Tex \LARGE \left(-8,-5\right)]. So this means that {{{x[1]=-8}}} and {{{y[1]=-5}}}.

Also, *[Tex \LARGE \left(x_{2}, y_{2}\right)] is the second point *[Tex \LARGE \left(-8,-9\right)].  So this means that {{{x[2]=-8}}} and {{{y[2]=-9}}}.



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



{{{m=(-9--5)/(-8--8)}}} Plug in {{{y[2]=-9}}}, {{{y[1]=-5}}}, {{{x[2]=-8}}}, and {{{x[1]=-8}}}



{{{m=(-4)/(-8--8)}}} Subtract {{{-5}}} from {{{-9}}} to get {{{-4}}}



{{{m=(-4)/(0)}}} Subtract {{{-8}}} from {{{-8}}} 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(-8,-5\right)] and *[Tex \LARGE \left(-8,-9\right)] is {{{x=-8}}}.



Any equation in the form x = k where k is some number CANNOT be written in the form {{{y-y[1]=m(x-x[1])}}}, which is why it is not possible to write the equation of the line through (-8, -5) and (-8, -9) in point-intercept form.