160 Chapter 3 Graphs, Relations, and Functions c. y = |x| 4 2 y 2 4 –2 –4 –2 –4 x Student Check 4 The points (3, 0), (0, -3), and (-4, 1) are solutions of the equation. Student Check 5 a. (1, -1) b. a 5 24 , -2b Student Check 6 a. i. (0, 4.0), (1, 4.7), (2, 5.8), (3, 6.0), (4, 5.5), (5, 5.1), (6, 4.6), (7, 4.6), (8, 5.8), (9, 9.3), (10, 9.6) SUMMARY OF KEY CONCEPTS 1. Ordered pairs (x, y) are plotted on a Cartesian coordinate system. • The x-value determines the movement from the origin on the x-axis. • The y-value determines how far up or down the point is located from the x-axis. • Quadrants are the four regions formed by the axes. Quadrant I is in the upper right, Quadrant II is in the upper left, Quadrant III is in the lower left, and Quadrant IV is in the lower right. • All points will lie in either one of the four quadrants or on one of the axes. 2. A solution of an equation in two variables is an ordered pair that makes the equation a true statement. ii. 10 0 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 0 0 Average Annual Unemployment Rate (2000–2010) 0 1 2 3 4 5 6 7 8 9 10 11 iii. The annual average unemployment rate increased slightly from 2000 to 2003 and then decreased until 2006. It remained unchanged through 2007 and then increased sharply until 2010. b. i. (125, 108), (150, 129), (175, 151), (200, 172) ii. 129 calories iii. (137.5, 118.5); A person who weighs 137.5 lb will burn 118.5 calories from a 30-min brisk walk. 3. To graph solutions of an equation, find several solutions of the equation by completing a table. Plot the solutions to obtain the graph. There can be infinitely many solutions of an equation in two variables. The graph is a picture of the solution set. 4. An ordered pair is a solution of an equation if it lies on the graph of the equation. 5. The midpoint of a line segment formed by two ordered pairs is found by averaging the x-coordinates and averaging the y-coordinates. 6. There are two main types of applications—using tables and using graphs. For each table given, write the paired data and then plot these points to create a scatter plot. For each given graph, write the ordered pairs that correspond to the points and answer questions about them. GRAPHING CALCULATOR SKILLS The graphing calculator can be used to plot points. This is a skill you will most likely need in later math courses. At this point, just know the feature is available but do not rely on this to plot points by hand. The graphing calculator can also be used to graph equations. Example 1: Plot the points (3, -2), (0, 4), and (-2, 0). Solution: Enter the x- and y-values into lists. Press STAT and 1 to access the list feature. Then enter the values in the appropriate columns, using L1 for the x-values and L2 for the y-values.
hendricks_intermediate_algebra_1e_ch1_3
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