Lines parallel to Axes

In three dimensional system, a line is formed by the set of points that satisfy the equation
r = r₀ + tv, where r = < x, y, z >, r₀ = < a, b, c >, v = < v₁, v₂, v₃ >. 

If two of the v_i = 0 and left one of v_i as nonzero, we get the equation becomes one of the parametric equations below.
To make it simple for beginner, we omit the the equation that contains the variable t. As such, the equation will look something like the set of equations below.

1. y = 3, z = -1
2. x = -2, z = 2
3. x = 1, y = 2

Take note that these types of lines are parallel to axes.

Let's learn to draw the lines which are parallel to the axes first.

If you wish to experience the forming of a line from a set of points, just click here for better viewing experience or move point P in the graph below. First, choose a line you wish from the left column below, the sliders show the coordinates of point P = (x, y, z). You may slide the values of x, y and/or z to view the changes on the line. 

Another point appears in the graph is the point on the coordinate plane. You will find that point P and the other point share at least two same values of x, y and z. For example, the green line that is parallel to z-axis passes through xy-plane at point C. Both point P and C have the same x and y values in their coordinates. Thus, the green line has the set of equations {x = 1, y = 2} in this case.



Betty, Created with GeoGebra, Screencast-O-Matic and Thomas Calculus, Pearson.