Question Video: Determining the Axis That Is Parallel to the Straight Line with the Given Equation Mathematics • 11th Grade

Video Transcript

Which axis is the straight line 𝑥 equals five parallel to?

Let’s think about the line with the equation 𝑥 equals five. And now the way of expressing this is the 𝑥-coordinate is five, which means that every point that lies on this line has an 𝑥-coordinate which is equal to five. Let’s think about what that would look like. Here we have a set of axes. The point with coordinates five, zero would be on this line. It has an 𝑥-coordinate of five and a 𝑦-coordinate of zero. The point with coordinates five, one would also be on this line. This point has an 𝑥-coordinate of five, and it has a 𝑦-coordinate of one. In the same way, the point with coordinates five, two also lies on the line.

Below the 𝑥-axis, the point with coordinates five, negative one will also lie on the line with equation 𝑥 equals five. And we can continue in this way in both directions. Connecting these points together, we see that the line with equation 𝑥 equals five is a vertical line passing through every point in the coordinate plane that has an 𝑥-coordinate of five. As this line is vertical, it is parallel to the 𝑦-axis.

In general, we can recall that lines with equations of the form 𝑥 equals 𝑘 for some constant value of 𝑘 are vertical lines which are parallel to the 𝑦-axis. On the other hand, lines with equations of the form 𝑦 equals 𝑐 for some constant 𝑐 are horizontal lines which are parallel to the 𝑥-axis. Our answer to the question “Which axis is the straight line 𝑥 equals five parallel to?” is the 𝑦-axis.