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