Answer:
x = 1
Explanation:
You want a line perpendicular to the horizontal line y=4, through the point (1, -1).
Perpendicular line
A line perpendicular to the standard form equation ...
ax +by = c
will have an equation of the form ...
bx -ay = c'
where c' is a constant that makes the line go through the desired point.
Application
Comparing the given equation to the standard form above, we have ...
ax +by = c
y = 4 ⇒ a=0, b=1, c=4
The perpendicular line will have the equation ...
1x -0y = c'
where c' is chosen to make the equation true for x=1, y=-1.
1(1) -0(-1) = c' = 1
The equation of the perpendicular line is x = 1.
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Additional comment
You can recognize that the given line (y=4) is a horizontal line, and the perpendicular will be the vertical line x=c for some constant c. That constant will be the x-value of the given point: 1. Then the perpendicular is ...
x = 1
Please note that the above approach to perpendicular lines is generally applicable. It works especially well with equations given in standard form, but can also work with equations given in other forms.
The slope of a perpendicular line is the opposite reciprocal of the slope of the original line. That relation can be used when the slope and its reciprocal are both defined. Here, the slope is zero, so its reciprocal is undefined, which can make the approach using slopes a bit confusing.