Question 124770
A vertical line has the characteristic that the x-coordinates of every point on the line are equal.  So the vertical line through (a, b) has an equation {{{x=a}}}.  Notice that y is not part of the equation.  That is because as long as {{{x=a}}}, the value of y can be any real number.  To put it another way, if you are given an equation that graphs to something other than a vertical line, and you choose a specific value for x, there will be exactly one corresponding value for y.  Not so with a vertical line -- for the single possible value for x there are infinite choices for y.  In your case, the equation would be {{{x=-45}}}.


Also, note that this equation is written in standard form ({{{ax+by=c}}}).  In your case, a = 1, b = 0, and c = -45.  This equation cannot be written in slope-intercept form.  Since all of the x-coordinates are equal, the denominator of the slope calculation would be zero ({{{(y[1]-y[2])/(x[1]-x[2])}}}), hence the slope is undefined.  If you cannot define m, you cannot write {{{y=mx+b}}}.  You also do not have an intercept because the vertical line is parallel to the y-axis and therefore never intersects it.


Contrast this with a horizontal line.  In a horizontal line, all of the y-coordinates are equal, regardless of the value of x.  So a horizontal line through (a, b) would be {{{y=b}}}.  x does not form part of the equation because it doesn't matter what x equals, y is always equal to b.