(7, -8) (7,7) slope: undefined
Y-intercept: none

Since the line is perfectly vertical, it's slope is infinite and, as you said, there's no defined y-intercept. Usually equations of lines are written in the form y = mx + b, but in the special case of a vertical line, the equation is written as x = c, where c is a constant. In this case, it would be x = 7. Like any line, it's comprised by all of the points which satisfy it's equation. In this case, all points with x-values of 7 are on the line. Y can be anything, all the way from -infinity to infinity.

Point A: (7,-8)
Point B: (7,7)

slope = m = rise / run = (y2 - y1) / (x2 - x1)
m = (7 - (-8)) / (7 - 7) = (7 + 8) / 0 = 15/0 = infinity

If you try to calculate 15 / 0, on your calculator,
you will get an error message, because 15 divided by 0
equals infinity. It's a good thing to remember: all vertical
lines have an infinite slope, while all horizontal lines
have a 0 (zero) slope.