01 Appendix Limits, Alternatives, and Choices Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin
Construction of a Graph Table Income Consumption Point $ 0 100 200 300 400 $ 50 100 150 200 250 a b c d e $400 300 200 100 Consumption (C) e d c b a $100 200 300 400 Income (Y) LO7 1App-2
Direct and Inverse Relationships Direct relationship Both variables move up or down together LO7 1App-3
Direct and Inverse Relationships Variables move opposite of each other LO7 1App-4
Positive slope of a straight line Slope of a Line Positive slope of a straight line Vertical Change +50 1 2 Slope = = = = 0.5 Horizontal Change +100 $400 300 200 100 Consumption (C) 50 Vertical Change 100 Horizontal Change $100 200 300 400 Income (Y) LO7 1App-5
Attendance (thousands) Slope of a Line Ticket Price Attendance (thousands) $50 40 4 30 8 20 12 10 16 LO7 1App-6
Negative slope of a straight line Slope of a Line Negative slope of a straight line Vertical Change -10 1 2 Slope = = -2 -2.5 = = 50 4030 20 10 Horizontal Change +4 Ticket Price $ Vertical Change -10 4 Horizontal Change 4 8 12 16 20 Attendance LO7 1App-7
Slopes and measurement units Slopes and marginal analysis Slope of a Line Slopes and measurement units Slopes and marginal analysis Infinite and zero slopes LO7 1App-8
Slope of a Line Slope = Zero Slope = Infinite Price of Bananas Consumption Watch Purchases Divorce Rate LO7 1App-9
Equation of a Linear Relationship 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 LO7 1App-10
Equation of a Line Y = 50 + .5C $400 300 Consumption (C) 200 100 Consumption (C) $100 200 300 400 Income (Y) LO7 1App-11
Equation of a Line P = 50 – 2.5Q 50 4030 20 10 Ticket Price 4 8 12 16 20 Attendance LO7 1App-12
Slope of a Nonlinear Curve Slope always changes Must use a line tangent to the curve to find the slope at that point LO7 1App-13
Slope of a Nonlinear Curve Use tangent lines to find the slope 20 15 10 5 5 10 15 20 LO7 1App-14