EDGE Math 8

The Rectangular Coordinate Plane (2)

Example

Plot the points in the following relation:
The relation T comprising all the points whose x-coordinate is any real number and whose y-coordinate is equal to one-half of the x-coordinate

Solution

Some ordered pairs belonging to T are $(- 5.8, - 2.9),$ $(- \sqrt{2}, - \frac{\sqrt{2}}{2}),$ $(- 1, - 0.5),$ $(1.2, 0.6),$ $(7, 3.5),$ and $(105, 52.5) .$ In fact, all the elements of S in the previous example are also in T. Notice that there are an infinite number of points in T. These points form a line as shown in the figure below.

Some relations are best described using an equation. In the preceding example, T can be written in symbols as follows:

T = {(x, y) | y = \frac{x}{2}} .

The equation above is read as "T is the set of all ordered pairs of real numbers $(x, y)$ such that $y = \frac{x}{2} ."$