Chapter 1 (Appendix) - Limits, alternatives, and choices. This chapter presents the following content: Construction of a graph, direct and inverse relationships, slope of a line, equation of a linear relationship, equation of a line, slope of a nonlinear curve.
01 Appendix Limits, Alternatives, and Choices McGrawHill/Irwin Copyright © 2012 by The McGrawHill Companies, Inc. All rights reserved Construction of a Graph Graph Table Consumption Point $ $ 50 a 100 100 b 200 300 150 c 200 d $400 Consumption (C) Income 300 e d 200 c 400 250 e 100 LO7 b a $100 200 300 400 Income (Y) 1App-2 Direct and Inverse Relationships • Direct relationship • LO7 Both variables move up or down together 1App-3 Direct and Inverse Relationships • Inverse relationship • LO7 Variables move opposite of each other 1App-4 Slope of a Line • Positive slope of a straight line Vertical Change +50 Slope = = = = 0.5 Horizontal Change +100 Consumption (C) $400 300 200 100 LO7 50 Vertical Change 100 Horizontal Change $100 200 300 Income (Y) 400 1App-5 Slope of a Line LO7 Ticket Price Attendance (thousands) $50 40 30 20 10 0 12 16 20 1App-6 Slope of a Line • Negative slope of a straight line Vertical Change -10 Slope = = = Horizontal Change +4 -2 = -2.5 50 Ticket Price $ 40 30 Vertical 20 Change -10 10 Horizontal Change 12 16 20 Attendance LO7 1App-7 Slope of a Line • • • LO7 Slopes and measurement units Slopes and marginal analysis Infinite and zero slopes 1App-8 Slope = Infinite Watch Purchases LO7 Consumption Price of Bananas Slope of a Line Slope = Zero Divorce Rate 1App-9 Equation of a Linear Relationship • • • • • LO7 y = a + bx y is the dependent variable a is the vertical intercept b is the slope of the line x is the independent variable 1App-10 Equation of a Line Consumption (C) Y = 50 + 5C $400 300 200 100 LO7 $100 200 300 Income (Y) 400 1App-11 Equation of a Line P = 50 – 2.5Q 50 Ticket Price 40 30 20 10 12 16 20 Attendance LO7 1App-12 Slope of a Nonlinear Curve • • LO7 Slope always changes Must use a line tangent to the curve to find the slope at that point 1App-13 Slope of a Nonlinear Curve • Use tangent lines to find the slope 20 15 10 5 LO7 10 15 20 1App-14 ... (C) Y = 50 + 5C $400 300 200 10 0 LO7 $10 0 200 300 Income (Y) 400 1App -1 1 Equation of a Line P = 50 – 2.5Q 50 Ticket Price 40 30 20 10 12 16 20 Attendance LO7 1App -1 2 Slope of a Nonlinear Curve... 20 10 0 12 16 20 1App-6 Slope of a Line • Negative slope of a straight line Vertical Change -1 0 Slope = = = Horizontal Change +4 -2 = -2 .5 50 Ticket Price $ 40 30 Vertical 20 Change -1 0 10 Horizontal... to the curve to find the slope at that point 1App -1 3 Slope of a Nonlinear Curve • Use tangent lines to find the slope 20 15 10 5 LO7 10 15 20 1App -1 4