Step by step
The question
Question: find the vertical line through (−3, 1), 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 (−3, 1).
So every point has the same x: −3.
So the line is x = −3.
x = −3 has no y in it.
So y can be any number.
But x is always −3.
2 Make points
Let's make some points.
Every point has x = −3.
For y, we pick any numbers: −3, −1 and 1.
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: (−3, −3),
(−3, −1),
and (−3, 1).
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 −3.
So x = −3 is a vertical line.
Careful: x = −3 is not a flat line.
It goes up and down.
5 Check
Let's check one more point on the line: (−3, −2).
Its x is −3.
So it fits x = −3.
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.