Section 2.1 Linear Equations in Two Variables 129 Points graphed in a rectangular coordinate system are defined by two numbers as an ordered pair (x, y).The first number (called the x-coordinate or abscissa) is the horizontal position from the origin. The second number (called the y-coordinate or ordinate) is the vertical position from the origin. Example 1 shows how points are plotted in a rectangular coordinate system. Plotting Points Example 1 Plot each point and state the quadrant or axis where it is located. a. (4, 1) b. (3, 4) c. (4,3) d. ( 2) e. (0, 3) f. (4, 0) Solution: a. The point (4, 1) is in quadrant I. b. The point (3, 4) is in quadrant . c. The point (4,3) is in quadrant IV. d. The point ( ) can also be written as 52 , 2 52 , (2.5,2).This point is in quadrant III. e. The point (0, 3) is on the y-axis. f. The point (4, 0) is on the x-axis. (3, 4) 5 4 (0, 3) (4, 1) 3 2 1 21 0 (4, 0) 543 1 2 3 4 5 1 2 3 4 5 (4, 3) Skill Practice Plot the point and state the quadrant or axis where it is located. 1. a. (3, 5) b. (2, 0) c. (2,1) d. (0, 4) e. (2,2) f. (5, 2) Answers 1. a. (3, 5); quadrant I b. (2, 0); x-axis c. (2,1); quadrant IV d. (0, 4); y-axis e. (2,2); quadrant III f. (5, 2); quadrant II (0, 4) 4 (3, 5) (5, 2) (2, 0) 543 1 2 3 4 5 2 3 4 5 (2, 1) (2, 2) 5 1 21 3 2 1 0 x y TIP: Notice that the points (3, 4) and (4, 3) are in different quadrants. Changing the order of the coordinates changes the location of the point. That is why points are represented by ordered pairs (Figure 2-3). x y 2 5 2 , Figure 2-3 2. Linear Equations in Two Variables Recall from Section 1.1 that an equation in the form is called a linear equation in one variable. In this section, we will study linear equations in two variables. ax b c Definition of a Linear Equation in Two Variables Let A, B, and C be real numbers such that A and B are not both zero.A linear equation in two variables is an equation that can be written in the form Ax By C This form is called standard form.
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