SECTION 3.2 Building Linear Models from Data 151 Point–slope form of a line Figure 7 (e) Nonlinear (d) Nonlinear (c) Nonlinear (b) Linear y 5 mx 1 b, m , 0 (a) Linear y 5 mx 1 b, m . 0 Distinguishing between Linear and Nonlinear Relations Determine whether the relation between the two variables in each scatter plot in Figure 8 is linear or nonlinear. EXAMPLE 2 Solution (a) Linear (b) Nonlinear (c) Nonlinear (d) Nonlinear Figure 8 (d) (c) (b) (a) Suppose that the scatter plot of a set of data indicates a linear relationship, as in Figure 7(a) or (b). We might want to model the data by finding an equation of a line that relates the two variables. One way to obtain a model for such data is to draw a line through two points on the scatter plot and determine an equation of the line. Now Work PROBLEM 5 Finding a Model for Linearly Related Data Use the data in Table 6 from Example 1. (a) Select two points and find an equation of the line containing the points. (b) Graph the line on the scatter plot obtained in Example 1(a). Solution EXAMPLE 3 (a) Select two points, say ( ) 31.5, 690 and ( ) 33.1, 778 . The slope of the line joining the points ( ) 31.5, 690 and ( ) 33.1, 778 is = − − = = m 778 690 33.1 31.5 88 1.6 55 An equation of the line with slope 55 and containing the point ( ) 31.5, 690 is found using the point–slope form with = = m x 55, 31.5, 1 and = y 690. 1 ( ) ( ) − = − − = − − = − = − y y m x x y x y x y x 690 55 31.5 690 55 1732.5 55 1042.5 1 1 = = = x y m 31.5, 690, 55 1 1 The Model (continued)
RkJQdWJsaXNoZXIy NjM5ODQ=