Copyright © 2007 Pearson Education, Inc. Slide 1-1
Copyright © 2007 Pearson Education, Inc. Slide 1-2 Chapter 1:Linear Functions, Equations, and Inequalities 1.1 Real Numbers and the Rectangular Coordinate System 1.2 Introduction to Relations and Functions 1.3 Linear Functions 1.4 Equations of Lines and Linear Models 1.5 Linear Equations and Inequalities 1.6 Applications of Linear Functions
Copyright © 2007 Pearson Education, Inc. Slide Equations of Lines and Linear Models Point-Slope Form of a Line Slope which can be rewritten as
Copyright © 2007 Pearson Education, Inc. Slide Examples Using Point-Slope Example 1 Using the Point-Slope Form –Find the slope-intercept form of the line passing through the points shown. (1, 7) and (3, 3) Solution
Copyright © 2007 Pearson Education, Inc. Slide Examples Using Point-Slope Example 2 Using the Point-Slope Form –The table below shows a list of points found on the line Find the equation of the line. Solution
Copyright © 2007 Pearson Education, Inc. Slide Equations of Lines in Ax + By = C Form Graphing an Equation in Form Graph Analytic Solution x-intercept: (2,0) y-intercept: (0,3) Graphing Calculator Solution
Copyright © 2007 Pearson Education, Inc. Slide Parallel Lines Two distinct nonvertical lines are parallel if and only if they have the same slope. Example Find the equation of the line that passes through the point (3,5) and is parallel to the line with equation Graph both lines in the standard viewing window. Solution Solve for y in terms of x.
Copyright © 2007 Pearson Education, Inc. Slide Parallel Lines
Copyright © 2007 Pearson Education, Inc. Slide Perpendicular Lines Two lines, neither of which is vertical, are perpendicular if and only if their slopes have a product of –1. Example Find the equation of the line that passes through the point (3,5) and is perpendicular to the line with equation Graph both lines in the standard viewing window. Use slopefrom the previous example. The slope of a perpendicular line is
Copyright © 2007 Pearson Education, Inc. Slide Perpendicular Lines
Copyright © 2007 Pearson Education, Inc. Slide Modeling Medicare Costs Linear Models and Regression –Discrete data points can be plotted and the graph is called a scatter diagram –Useful when analyzing trends in data –e.g. Estimates for Medicare costs (in billions) x (Year)y (Cost)
Copyright © 2007 Pearson Education, Inc. Slide Modeling Medicare Costs a)Scatter diagram where x = 0 corresponds to 2002, x = 1 to 2003, etc. Data points (0, 264), (1, 281), (2, 299), (3, 318), (4, 336) and (5, 354) b)Linear model – pick 2 points, (0, 264) and (3, 318) c)Predict cost of Medicare in 2010
Copyright © 2007 Pearson Education, Inc. Slide The Least-Squares Regression Line –Enter data into lists L1 (x list) and L2 (y list) –Least-squares regression line: LinReg in STAT/CALC menu
Copyright © 2007 Pearson Education, Inc. Slide Correlation Coefficient Correlation Coefficient r –Determines if a linear model is appropriate range of r: r near +1, low x-values correspond to low y-values and high x-values correspond to high y-values r near –1, low x-values correspond to high y-values and high x-values correspond to low y-values means there is little or no correlation –To calculate r with the TI-83, turn Diagnostic On in the Catalog menu
Copyright © 2007 Pearson Education, Inc. Slide Application of Least-Squares Regression Example Predicting Airline Passenger Growth Harrisburg International Dayton International Austin Robert Mueller Milwaukee General Mitchell Sacramento Metropolitan Fort Lauderdale-Hollywood Washington Dulles Greater Cincinnati Airline Passengers (millions) Airport
Copyright © 2007 Pearson Education, Inc. Slide Application of Least-Squares Regression Scatter Diagram Linear Regression: Prediction for 2005 at Raleigh-Durham International using this model: FAA’s prediction: 10.3 million