What is the equation for a line in slope intercept form passing through (2,11) and perpenduclar to y =4

Answer 1

y=4 is a horizontal line, since the slope is zero, i.e.
y=0x+4.
A line perpendicular to a horizontal line is vertical.
The equation for a vertical line is
x=k
If the line passes through (2,11), then k=2.
Therefore the required line is x=2.

Answer 2

y = 4 is a horizontal line. A line prependicular to it will be vertical, which means that x must be constant. The "slope" m of a vertical line is infinity.

Therefore the equation for the line is x = 2, regardless of the value of y. Slope-intercept format cannot be used when the slope is infinite.