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Section 3.1 Equations and the Rectangular Coordinate System 197 The signs of a point’s coordinates determine where on the plane the point is located. • If both the x- and y-coordinates are positive, the point lies in Quadrant I. • If the x-coordinate is negative and the y-coordinate is positive, the point lies in Quadrant II. • If both the x- and y-coordinates are negative, the point lies in Quadrant III. • If the x-coordinate is positive and the y-coordinate is negative, the point lies in Quadrant IV. • If both the x- and y-coordinates are 0, the point lies on both the x- and y-axes (or at the origin). • If the x-coordinate is 0 and the y-coordinate is nonzero, the point lies on the y-axis. • If the x-coordinate is nonzero and the y-coordinate is 0, the point lies on the x-axis. �� ������������������������ ������������������ Plot each ordered pair on the Cartesian coordinate system and state the quadrant or axis where each point is located. 2a. (4, 3) 2b. (-2, 5) 2c. (5, -2) 2d. (0, 4) 2e. (-3, 0) 2f. a- 3 2 , - 8 2 b Solutions 2a. To plot (4, 3), move 4 units right from the origin and 3 units up. (4, 3) is located in Quadrant I. 2b. To plot (-2, 5), move 2 units left from the origin and 5 units up. (-2, 5) is located in Quadrant II. 2c. To plot (5, -2), move 5 units right from the origin and 2 units down. (5, -2) is located in Quadrant IV. 2d. To plot (0, 4), do not move left or right, move 4 units up. (0, 4) is located on the y-axis. (–2, 5) 2e. To plot (-3, 0), move 3 units left from the origin and do not move up or down. (-3, 0) is located on the x-axis. 2f. The point a- 3 2 , - 8 3 b = (-1.5, -2.7). Move 1.5 units left from the origin and 2.7 units down. a- 3 2 , - 8 3 b is located in Quadrant III. ������������ The points (-2, 5) and (5, -2) illustrate the fact that the order is important. Changing the order of the numbers in the ordered pairs changes the location of the point. Student Check 2 Plot each ordered pair on the Cartesian coordinate system and state the quadrant or axis where each point is located. a. (-5, -1) b. (3, -4) c. (-4, 3) d. (0, -2) e. (1, 0) f. a1 2 , 5 4 b Graphing Equations The graph of an equation is a picture of all the ordered pairs that satisfy the equation. When an equation contains two variables, there are infinitely many ordered pairs that satisfy the equation. It is impossible to find every solution of an equation in two variables. So, we plot several ordered pairs (solutions) to get an idea of the graph’s shape. Recall in Chapter 1 that we evaluated algebraic expressions and recorded our results in a table. We use the table again to record the values for x and y. Objective 3 ▶ Graph the solutions of an equation. (–3, 0) (0, 4) (4, 3) (5, –2) 2 2 4 4 –2 –4 –2 –4 32 83 – ,– x y


hendricks_beginning_algebra_1e_ch1_3
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