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 xcoordinate 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 xcoordinate 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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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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