152 Chapter 2 Linear Equations in Two Variables and Functions Number (millions) 70 60 50 40 30 20 10 0 Number of Males 20 Years or Older Employed Full-Time in the United States (1970, 43.0) 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 1x1, y1 1x2, y22 2 m m y2 y1 x2 x1 22.4 35 65.4 43.0 2005 1970 or m 0.64 22.4 35 TIP: The slope, m , means that the workforce increased by 22.4 million men over 35 yr. This is the same 0.64 rate as , meaning that 1 the workforce increased by 0.64 million men per year. Section 2.2 Practice Exercises Figure 2-22 Source: U.S. Census Bureau (2005, 65.4) a. Find the slope of the line, using the points (1970, 43.0) and (2005, 65.4). b. Interpret the meaning of the slope in the context of this problem. Solution: a. 11970, 43.02 and 12005, 65.42 Label the points. Apply the slope formula. b. The slope is approximately 0.64, meaning that the full-time workforce has increased at a rate of 0.64 million men (or 640,000 men) per year between 1970 and 2005. Skill Practice The number of people per square mile (called population density) in Alaska has increased linearly since 1990. In 1990, there were 0.96 people per square mile. By 2010, this increased to 1.32 people per square mile. 9. Find the slope of the line passing through the points (1990, 0.96) and (2010, 1.32). 10. Interpret the meaning of the slope in the context of this problem. Answers 9. 0.018 10. The population density increased at a rate of 0.018 people per square mile per year. Study Skills Exercise Instructors vary in what they emphasize on tests. For example, test material may come from the textbook, notes, handouts, and homework.What did your instructor emphasize on the last test? Vocabulary and Key Concepts 1. a. The ratio of the vertical change and the horizontal change between two distinct points (x1, y1) and (x2, y2) on a line is called the of the line.The slope can be computed from the formula m . b. Lines in the same plane that do not intersect are called lines. Such lines, if they are nonvertical, have the slope and different y-intercepts. c. Two lines are perpendicular if they intersect at a angle. d. If m1 and m2 represent the slopes of two nonvertical perpendicular lines, then m1 m2 .
miller_intermediate_algebra_4e_ch1_3
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