By Berchie Holliday
Ebook via Holliday, Berchie, Cuevas, Gilbert J., McClure, Melissa S.
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Additional resources for Advanced Mathematical Concepts: Precalculus with Applications
B. Use two ordered pairs to write the equation of a best-fit line. c. Use a graphing calculator to find an equation of the regression line for the data. What is the correlation coefficient? d. If the equation of the regression line shows a moderate or strong relationship, predict the missing value. Explain whether you think the prediction is reliable. 4. Economics The table shows the average amount that an American spent on durable goods in several years. Personal Consumption Expenditures for Durable Goods Year 1990 1991 1992 1993 1994 1995 1996 1997 2010 Personal Consumption ($) 1910 1800 1881 2083 2266 2305 2389 2461 ?
This problem will be solved in Example 2. • Graph linear equations. • Find the x- and y-intercepts of a line. • Find the slope of a line through two points. • Find zeros of linear functions. The problem above can be solved by using a linear equation. A linear equation has the form Ax ϩ By ϩ C ϭ 0, where A and B are not both zero. Its graph is a straight line. The graph of the equation 3x ϩ 4y Ϫ 12 ϭ 0 is shown. y 3x ϩ 4y Ϫ 12 ϭ 0 O x Example The solutions of a linear equation are the ordered pairs for the points on its graph.
The slopes of two nonvertical parallel lines are equal. The graphs of two equations that represent the same line are said to coincide. Parallel Lines y O x Two nonvertical lines in a plane are parallel if and only if their slopes are equal and they have no points in common. Two vertical lines are always parallel. We can use slopes and y-intercepts to determine whether lines are parallel. Example 1 Determine whether the graphs of each pair of equations are parallel, coinciding, or neither. a. 3x Ϫ 4y ϭ 12 9x Ϫ 12y ϭ 72 y O Write each equation in slope-intercept form.
Advanced Mathematical Concepts: Precalculus with Applications by Berchie Holliday