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

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.

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.

To find the equation of a line that is perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.

Given that the equation of the line is y = 4, we can see that the slope of this line is 0 since it is a horizontal line.

For a line perpendicular to a horizontal line with slope 0, the slope of the new line will be undefined or represented as a vertical line.

Now, let's find the equation for the perpendicular line passing through the point (2,11) using the point-slope form, y - y₁ = m(x - x₁), where (x₁, y₁) = (2,11) and m is the slope.

Since the slope is undefined, we can write the equation using the x-coordinate of the given point (2,11):
x = 2

Therefore, the equation for the line passing through (2,11) and perpendicular to y = 4 is x = 2.