222 Chapter 2 Linear Equations in Two Variables and Functions Section 2.4 Applications of Linear Equations and Modeling Key Concepts A linear model can be constructed to describe data for a given situation. • Given two points from the data, use the point-slope formula to find an equation of the line. • Interpret the meaning of the slope and y-intercept in the context of the problem. • Use the equation to predict values. Examples Example 1 The per capita income in the United States has been rising linearly since 1980. In the graph, x represents the number of years since 1980, and y represents average income in dollars. 40,000 30,000 20,000 10,000 Per Capita Yearly Income in the United States (25, 26,100) (5, 11,000) 0 0 10 20 30 40 Dollars ($) Year (x 5 0 represents 1980) Write an equation of the line, using the points (5, 11,000) and (25, 26,100). Slope: 26,100 11,000 25 5 y 11,000 7551x 52 y 11,000 755x 3775 y 755x 7225 15,100 20 755 • The slope 755 indicates that the average income has increased at a rate of $755 per year. • The y-intercept (0, 7225) means that the average income in 1980 (year x = 0) was $7225. By substituting different values of x, the equation can be used to approximate the average income for that year. For the year 2010 (x 30), we have: y 7551302 7225 y 29,875 The average per capita income in 2010 would be approximately $29,875.
miller_intermediate_algebra_4e_ch1_3
To see the actual publication please follow the link above