What is the equation of a vertical line that has an x-intercept of -2?

As the line is vertical, it has same points for x - coordinates. And it never changes for whole line.
We know, slope (m) = y2 - y1 / x2 - x1
As x2-x1 = 0  [ x2=x1 ]

m = y2-y1 / 0
m = undefined

So, y = mx + c
y = c

In short, Your Answer would be y = c

Hope this helps!