Step by step
The question
Question: find the line through (1, −2), parallel to x = 3.
x = 3
new line: through (1, −2)
parallel to this one
1 Slope of the given line
x = 3 is a vertical line: straight up and down.
We call its slope undefined.
m = undefined
2 Slope of the new line
The given line is vertical.
A parallel line is vertical too.
3 Write the equation
A vertical line through (1, −2): every point on it has the same x.
So x = 1.
x = 1
4 Check
Let's see it on the grid.
The given line in blue.
Our new line x = 1 in red.
It goes through (1, −2).
They never meet.
Let's look back.
First: slope of the given line.
Then: slope of the new line.
Then: write the equation.
Last: check.
Answer
x = 1