204 Chapter 3 Linear Equations in Two Variables ANSWERS TO STUDENT CHECKS Student Check 1 a. no b. yes c. yes Student Check 2 a. Quadrant III b. Quadrant IV c. Quadrant II d. y-axis e. x-axis f. Quadrant I Student Check 3 a. b. (2, 1) 4 (–1, –2) (0, –1) (–2, –3) (1, 0) 2 –4 –2 4 6 –4 x y 4 2 f. 12 54 , e. (1, 0) (–1, 1) (1, 1) 2 4 4 –2 –4 –2 –4 x y (–2, 4) (2, 4) c. (–2, 3) 2 (–1, 2) (0, 1) (2, 1) 2 4 4 6 –2 –4 –2 –4 x y Student Check 4 a. yes b. no c. yes d. no e. yes Student Check 5 a. i. (0, 653), (1, 862), (2, 911), (3, 819), (4, 804) ii. The first point means that in 0 yr after 2000, in the year 2000, there were 653 murder victims by juvenile gang killings. The last point means that in 4 yr after 2000, in the year 2004, there were 804 murder victims by juvenile gang killings. iii. The scatter plot is 950 900 850 800 750 700 600 0 1 2 3 4 5 650 b. i. (amazon.com, 71), (barnesandnoble.com, 8), (bestbuy.com, 17), (ebay.com, 65), (gap.com, 6), (homedepot.com, 12), ( jcpenney.com, 14), (macys.com, 9), (sears.com, 13), (staples.com, 8), (target.com, 28), (walmart.com, 35), (zappos.com, 6) ii. The website with the largest number of visitors in August 2010 was amazon.com. The site had 71 million visitors. iii. The websites with the least number of visitors in August 2010 were gap.com and zappos.com, each with 6 million visitors. SUMMARY OF KEY CONCEPTS 1. A solution of an equation in two variables is an ordered pair that makes the equation a true statement. 2. Ordered pairs can be 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. Points will lie in either one of the four quadrants or on one of the axes. 3. To graph solutions of an equation, find several solutions of the equation by completing a table. Plot the solutions and then connect them to form the graph. There are infinitely many solutions of an equation in two variables. The graph is a picture of these solutions. 4. We can determine if an ordered pair is a solution of an equation if it lies on the graph of the equation. 5. For application problems, it is important to understand what the x- and y-coordinates represent. If the data are given in a table, bar graph, or line graph, the set of ordered pairs is called paired data. Graphing paired data gives us a scatter plot of the data. 2 4 –2 –4 –2 –4 x y c. (–4, 3) a. (–5, –1) d. (0, –2) b. (3, –4)
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