Step by step
The question
Question: find the line through (2, 3), perpendicular to y = 4.
y = 4
new line: through (2, 3)
perpendicular to this one
1 Slope of the given line
There is no x term.
So m = 0: a flat line.
b is 4.
m = 0
b = 4
2 Slope of the new line
The given line is flat: slope 0.
0 cannot be flipped.
At a square corner to a flat line is a vertical line.
3 Write the equation
A vertical line through (2, 3): every point on it has the same x.
So x = 2.
x = 2
4 Check
Let's see it on the grid.
The given line in blue.
Our new line x = 2 in red.
It goes through (2, 3).
They meet at a square corner.
Let's look back.
First: slope of the given line.
Then: slope of the new line.
Then: write the equation.
Last: check.
Answer
x = 2