Step by step
The question
Question: find the vertical line through (4, −2), and graph it.
A new word: vertical.
It means straight up and down.
1 Write the equation
A vertical line goes straight up and down.
Every point on it is right above or below (4, −2).
So every point has the same x: 4.
So the line is x = 4.
x = 4 has no y in it.
So y can be any number.
But x is always 4.
2 Make points
Let's make some points.
Every point has x = 4.
For y, we pick any numbers: −4, −2 and 2.
3 Plot the points
Draw the grid.
The x-axis goes across.
The y-axis goes up and down.
They meet at 0.
That point is called the origin.
Put the points on the grid: (4, −4),
(4, −2),
and (4, 2).
They stand in a column, right above each other.
4 Draw the line
Join the dots.
The line goes straight up and down.
It is a vertical line.
It never goes across, so we call its slope undefined.
It crosses the x-axis at 4.
So x = 4 is a vertical line.
Careful: x = 4 is not a flat line.
It goes up and down.
5 Check
Let's check one more point on the line: (4, 1).
Its x is 4.
So it fits x = 4.
The line is right!
Let's look back.
First: write the equation.
Then: make points.
Then: plot the points.
Then: draw the line.
Last: check.