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Chapter 8

Chapter 8. Graphs, Functions, and Systems of Equations and Inequalities. Chapter 8: Graphs, Functions, and Systems of Equations and Inequalities. 8.1 The Rectangular Coordinate System and Circles 8.2 Lines, Slope, and Average Rate of Change 8.3 Equations of Lines and Linear Models

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Chapter 8

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  1. Chapter 8 Graphs, Functions, and Systems of Equations and Inequalities 2012 Pearson Education, Inc.

  2. Chapter 8: Graphs, Functions, and Systems of Equations and Inequalities • 8.1 The Rectangular Coordinate System and Circles • 8.2 Lines, Slope, and Average Rate of Change • 8.3 Equations of Lines and Linear Models • 8.4 An Introduction to Functions: Linear Functions, Applications, and Models • 8.5 Quadratic Functions, Graphs, and Models • 8.6 Exponential and Logarithmic Functions, Applications, and Models • 8.7 Systems of Equations • 8.8 Applications of Systems • 8.9 Linear Inequalities, Systems, and Linear Programming 2012 Pearson Education, Inc.

  3. Section 8-3 • Equations of Lines and Linear Models 2012 Pearson Education, Inc.

  4. Equations of Lines and Linear Models • Point-Slope Form • Slope-Intercept Form • Summary of Forms and Linear Equations • Linear Models 2012 Pearson Education, Inc.

  5. Point-Slope Form The equation of the line through (x1, y1) with slope m is written in point-slope form as 2012 Pearson Education, Inc.

  6. Example: Finding an Equation Given the Slope and a Point Find the standard form of an equation of the line with slope 1/3, passing through the point (–3, 2). Solution Multiply by 3 Standard form 2012 Pearson Education, Inc.

  7. Example: Finding an Equation Given Two Points Find the standard form of an equation of the line with passing through the points (2, 1) and (–1, 3). Solution Find the slope. Use either point in the form. Standard form 2012 Pearson Education, Inc.

  8. Slope-Intercept Form The equation of the line with slope m and y-intercept (0, b) is written in slope-intercept form as Slope y-intercept 2012 Pearson Education, Inc.

  9. Example: Graphing Using Slope and the y-Intercept Graph the line with equation y Solution Plot the intercept (0, –2) and use the slope: rise 3, run 2. run 2 x rise 3 (0, –2) 2012 Pearson Education, Inc.

  10. Summary of Forms of Linear Equations Standard form Vertical line Horizontal line Slope-intercept form Point-Slope form 2012 Pearson Education, Inc.

  11. Linear Models Earlier examples gave equations that described real data. The process of writing an equation to fit a graph is called curve-fitting. The next example illustrates this concept for a straight line. The resulting equation is called a linear model. 2012 Pearson Education, Inc.

  12. Example: Modeling Costs Estimates for Medical costs (in billions of dollars) are shown below. a) Find a linear equation that models the data. b) Use the model to predict the costs in 2010. 2012 Pearson Education, Inc.

  13. Example: Medical Costs Solution Let x = 0 correspond to 2000, x = 1 correspond to 2001, and so on. We can express the data as ordered pairs: (0, 225), (1, 243), (2, 261), (3, 279), and (4, 297). a) To find a linear equation through the data we choose two points to get the slope. Using (0, 225) and (3, 279): 2012 Pearson Education, Inc.

  14. Example: Medical Costs Solution(continued) Now since we have the y-intercept (0, 225) we have the equation b) The value x = 10 corresponds to the year 2010. When x = 10, The model predicts that the costs will be $405 billion in 2010. 2012 Pearson Education, Inc.

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