Question

slope of x=-7..........the lope is undefined, right?

Answer 1

yes. the slope is how many you have to move up, as you move across one unit to the right,
x=-7,
moving one unit to the right is impossible if you are on this line
so yeah either infinite slope or undefined slope

Answer 2

slope of x=-7

x = -7 is a vertical line and the slope is undefined.