The Rectangular Coordinate System As mentioned, there are infinitely many solutions of equations in two variables. Our ultimate goal is to visualize the solutions of these types of equations. Recall that we use a real number line to visualize solutions of equations and inequalities in one variable. To graph solutions of equations in two variables, we need a special system, called the rectangular coordinate system or the Cartesian coordinate system. The rectangular coordinate system consists of two real number lines intersecting at right angles. The horizontal number line is referred to as the x-axis and the vertical number line is referred to as the y-axis. The point where the two number lines intersect is called the origin. Every point on the coordinate system has an “address.” This address is denoted by an ordered pair (x, y). Each point on the plane is determined by knowing how far left or right the point is from the origin and how far up or down the point is located from the x-axis. In an ordered pair (x, y), the value x is called the first coordinate or x-coordinate. The x-coordinate tells us how far left (if x is negative) or right (if x is positive) to move from the origin. The value y is called the second coordinate or y-coordinate. The y-coordinate tells us how far up (if y is positive) or down (if y is negative) to move from the x-axis. For example, in the ordered pair (4, 5), 4 is the x-coordinate → move from the origin 4 units right 5 is the y-coordinate → move from the position on the x-axis 5 units up Note that the ordered pair (5, 4) is different than (4, 5). For the point (5, 4), we move 5 units to the right and 4 units up. ���������������������� Plotting an Ordered Pair Step 1: From the origin, move left or right to the given x-value in the ordered pair. Step 2: From this x-value, move up or down to the given y-value in the ordered pair. Step 3: The point is located at the result of the two movements. The two numbers lines that form the Cartesian coordinate system divide the plane into four regions called quadrants. We label these four quadrants with Roman numerals I, II, III, and IV beginning in the upper right quadrant and rotating counterclockwise. 6 2 2 4 4 6 –2 (a, 0) –6 –4 –2 –4 –6 x y Quadrant II (–, +) Quadrant I (+, +) (+, –) Quadrant IV (–, –) Quadrant III (0, b) Objective 2 ▶ Plot ordered pairs and identify quadrants. x y 2 2 4 4 –2 –4 –2 –4 (4, 5) Origin 196 Chapter 3 Linear Equations in Two Variables
hendricks_beginning_algebra_1e_ch1_3
To see the actual publication please follow the link above