Horizontal and vertical lines: y = 3 and x = −2

0:00What does the graph of y equals 3 look like? Let's plot some points and see.

0:06Each point is an ordered pair, x then y: x tells you how far across, and y how far up.

0:15Start with negative 2, 3. From the origin, where the axes cross, go 2 left, then 3 up.

0:26Now plot 0, 3 and 4, 3. Each is also 3 units up.

0:33The second number in each pair is the y-coordinate. Here it is 3, 3 and 3.

0:42Join the points. They make a horizontal line, one that runs straight across.

0:48Other points on it, like 2, 3 or negative 3, 3, also have a y-coordinate of 3.

0:55Whatever x is, y is always 3, so the equation of this line is y equals 3.

1:03A common mistake is drawing y equals 3 as a vertical, up-and-down line through 3 on the x-axis.

1:11But points on that line, like 3, 1 and 3, 4, have 3 as their first number, the x-coordinate. So it is the line x equals 3.

1:23Now keep x the same instead. Plot negative 2, negative 1 and negative 2, 1.

1:30With negative 2, 3 from before, the x-coordinate is negative 2 every time.

1:36Join them. They make a vertical line, straight up and down, with the equation x equals negative 2.

1:44The two lines cross at negative 2, 3, where x is negative 2 and y is 3.

1:51So y equals 3 is a horizontal line, and x equals negative 2 is a vertical line.