By Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
This obtainable textual content is designed to aid readers aid themselves to excel. The content material is equipped into elements: (1) A Library of trouble-free features (Chapters 1–2) and (2) Calculus (Chapters 3–9). The book’s total strategy, subtle via the authors’ event with huge sections of faculty beginners, addresses the demanding situations of educating and studying while readers’ prerequisite wisdom varies vastly. Reader-friendly beneficial properties akin to Matched difficulties, discover & talk about questions, and Conceptual Insights, including the motivating and considerable functions, make this article a well-liked selection for today’s scholars and instructors.
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Additional resources for Calculus for Business, Economics, Life Sciences and Social Sciences (12th Edition) (Barnett)
Published by Pearson. Copyright © 2010 by Pearson Education, Inc. SECTION 1-2 Graphs and Lines 13 1-2 Graphs and Lines Cartesian Coordinate System Graphs of Ax + By = C Slope of a Line Equations of Lines: Special Forms Applications In this section, we will consider one of the most basic geometric figures a line. When we use the term line in this book, we mean straight line. We will learn how to recognize and graph a line, and how to use information concerning a line to find its equation. Examining the graph of any equation often results in additional insight into the nature of the equation s solutions.
Assume that cost C is linearly related to output x. (A) Find the slope of the line joining the points associated with outputs of 0 and 100; that is, the line passing through (0, 300) and (100, 4,300). (B) Find an equation of the line relating output to cost. Write the final answer in the form C = mx + b. (C) Graph the cost equation from part (B) for 0 SOLUTION x 200. y2 - y1 x2 - x1 4,300 - 300 = 100 - 0 4,000 = = 40 100 (A) m = (B) We must find an equation of the line that passes through (0, 300) with slope 40.
EXAMPLE 6 Using the Point-Slope Form (A) Find an equation for the line that has slope 12 and passes through ( -4, 3). Write the final answer in the form Ax + By = C. (B) Find an equation for the line that passes through the points (-3, 2) and (-4, 5). Write the resulting equation in the form y = mx + b. SOLUTION (A) Use y - y1 = m(x - x1). Let m = y - 3 y - 3 2y - 6 -x + 2y 1 2 [x 1 2 (x 1 2 and (x1, y1) = (- 4, 3). Then - ( -4)] = + 4) = = x + 4 = 10 or x - 2y = - 10 Multiply both sides by 2. Calculus for Business, Economics, Life Sciences and Social Sciences, Twelfth Edition, by Raymond A.