Step by step
The question
Question: find the horizontal line through (3, −1), and graph it.
A new word: horizontal.
It means flat, going across.
1 Write the equation
A horizontal line is flat.
Every point on it is right beside (3, −1), at the same height.
So every point has the same y: −1.
So the line is y = −1.
y = −1 has no x in it.
So x can be any number.
But y is always −1.
2 Make points
Let's make some points.
Every point has y = −1.
For x, we pick any numbers: −1, 1 and 3.
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: (−1, −1),
(1, −1),
and (3, −1).
They stand in a row, right beside each other.
4 Draw the line
Join the dots.
The line goes flat, across.
It is a horizontal line.
It never goes up, so its slope is 0.
It crosses the y-axis at −1.
So y = −1 is a horizontal line.
Careful: y = −1 does not go up and down.
It is flat.
5 Check
Let's check one more point on the line: (2, −1).
Its y is −1.
So it fits y = −1.
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.