Example 122 graph the relation r x y 1 y 3 solution

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Unformatted text preview: ve seen equations like this before. Depending on the context, ‘x = 3’ could mean we have solved an equation for x and arrived at the solution x = 3. In this case, however, ‘x = 3’ describes a set of points in the plane whose x-coordinate is 3. Similarly, the equation y = −2 in this context corresponds to all points in the plane whose y -coordinate is −2. Since there are no restrictions on the x-coordinate listed, we would graph the relation y = −2 as the horizontal line above on the right. In general, we have the following. 1.2 Relations 17 Equations of Vertical and Horizontal Lines • The graph of the equation x = a is a vertical line through (a, 0). • The graph of the equation y = b is a horizontal line through (0, b). In the next section, and in many more after that, we shall explore the graphs of equations in great detail.2 For now, we shall use our final example to illustrate how relations can be used to describe entire regions in the plane. Example 1.2.2. Graph the relation: R = {(x, y ) : 1 < y ≤ 3} Sol...
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