## Monday, November 12, 2012

Sometimes there is confusion among students when graphing lines such as x = 5 and y = 4.

The x-axis is the horizontal axis and the y-axis is the vertical axis, yet the graph of x = 5 is a vertical line through 5 on the x-axis. Likewise the graph of y = 4 is a horizontal line through 4 on the y-axis.
This seems to be opposite of what one might expect, but there is a simple reason for this.

For the line x =5, think first of the point (5,0). Now draw the vertical line through this point and pick another point on the line, for instance (5,2), another point would be (5, -1) and so on. Notice that for every point, the only value that changes is the y coordinate, the x coordinate is always 5.  So the vertical line is correct because the x coordinate for every point on that line is 5. The slope of a vertical line is undefined.

The same argument holds true for the equation y = 4.  It's a horizontal line because for every point on that line, the y coordinate is 4.  The point (0,4) is on the line, as are points (1, 4), (-2, 4) and so on.