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Use the rectangular coordinate system to uniquely identify points in a plane using ordered pairs (x, y). Ordered pairs indicate position relative to the origin. The x -coordinate indicates position to the left and right of the origin. The y -coordinate indicates position above or below the origin.
- Plotting Points in a Rectangular Coordinate System. Plot the points ( −2,4 ), ( −2,4 ), ( 3,3 ), ( 3,3 ), and ( 0,−3 ) ( 0,−3 ) in the plane. Solution.
- Graphing an Equation in Two Variables by Plotting Points. Graph the equation y=−x+2 y=−x+2 by plotting points. Solution. First, we construct a table similar to Table 2.
- Using a Graphing Utility to Graph an Equation. Use a graphing utility to graph the equation: y=− 2 3 x+ 4 3 . y=− 2 3 x+ 4 3 . Solution. Enter the equation in the y= function of the calculator.
- Finding the Intercepts of the Given Equation. Find the intercepts of the equation y=−3x−4. y=−3x−4. Then sketch the graph using only the intercepts.
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Aug 15, 2020 · On the horizontal axis, the positive direction is to the right, negative is to the left. On the vertical axis, the positive direction is up, negative is down. The point (0, 0) is called the origin of the coordinate system, and is the starting point for all point plotting.
The idea of coordinate geometry is to use algebra so that you can do calculations like this when A and B are any points, and not just the particular points in Fig. 1.1. It often helps to use a notation which shows at a glance which point a coordinate refers to. One way of doing this is with suf xes, calling the coordinates of the rst point (x 1 ...
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Example 1 Plot the point A(−3, 4) in a coordinate plane. Describe the location of the point. Start at the origin. Move 3 units left and 4 units up. Then plot the point. The point is in Quadrant II. x y 4 2 −4 −2 −4 −2 2 4 A(−3, 4) −3 4 Plot the point in a coordinate plane. Describe the location of the point. 1. A(3, 2) 2. B(−5 ...
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2. matrix. This is the key question, and Chapter 6 will answer. it properly. We will find the equation for the eigenvalues of any matrix (Section 6.1). We. will test those eigenvalues for stability (Section 6.4). Eigenvalues and eigenvectors are. a major topic, the most important link between differential equations and linear algebra.
