Question 121924
First lets find the slope through the points ({{{4}}},{{{4}}}) and ({{{4}}},{{{2}}})

{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula (note: *[Tex \Large \left(x_{1},y_{1}\right)] is the first point ({{{4}}},{{{4}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{4}}},{{{2}}}))

{{{m=(2-4)/(4-4)}}} Plug in {{{y[2]=2}}},{{{y[1]=4}}},{{{x[2]=4}}},{{{x[1]=4}}}  (these are the coordinates of given points)

{{{m= -2/0}}} Subtract the terms in the numerator {{{2-4}}} to get {{{-2}}}.  Subtract the terms in the denominator {{{4-4}}} to get {{{0}}}

Since the denominator is zero, the slope is undefined (remember you cannot divide by zero). So we cannot use the slope intercept form to write an equation. So we can only say that the equation is a vertical line through {{{x=4}}}, which means the equation is {{{x=4}}} (notice this is <font size=4><b>not</b></font> in slope-intercept form)

So the equation {{{x=4}}} looks like this:

{{{drawing(500, 500, -5, 13, -6, 12,
graph(500, 500, -5, 13, -6, 12,1000(x-4)),
circle(4,4,0.1),
circle(4,4,0.1+0.03),
circle(4,2,0.1),
circle(4,2,0.1+0.03)
) }}} Graph of {{{x=4}}} through the points ({{{4}}},{{{4}}}) and ({{{4}}},{{{2}}})