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Linear Functions and Models

Linear Functions and Models. Lesson 2.1. Problems with Data. Real data recorded Experiment results Periodic transactions Problems Data not always recorded accurately Actual data may not exactly fit theoretical relationships In any case …

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Linear Functions and Models

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  1. Linear Functions and Models Lesson 2.1

  2. Problems with Data • Real data recorded • Experiment results • Periodic transactions • Problems • Data not always recorded accurately • Actual data may not exactly fit theoretical relationships • In any case … • Possible to use linear (and other) functions to analyze and model the data

  3. Fitting Functions to Data • Consider the data given by this example • Note the plot ofthe data points • Close to beingin a straight line

  4. Finding a Line to Approximate the Data • Draw a line “by eye” • Note slope, y-intercept • Statistical process (least squares method) • Use a computer programsuch as Excel • Use your TI calculator

  5. Graphs of Linear Functions • For the moment, consider the first option Given the graph with tic marks = 1 • Determine • Slope • Y-intercept • A formula for the function • X-intercept (zero of the function)

  6. Graphs of Linear Functions • Slope – use difference quotient • Y-intercept – observe • Write in form • Zero (x-intercept) – what value of x gives a value of 0 for y?

  7. Modeling with Linear Functions • Linear functions will model data when • Physical phenomena and data changes at a constant rate • The constant rate is the slope of the function • Or the m in y = mx + b • The initial value for the data/phenomena is the y-intercept • Or the b in y = mx + b

  8. Modeling with Linear Functions • Ms Snarfblat's SS class is very popular. It started with 7 students and now, 18 months later has grown to 80 students. Assuming constant monthly growth rate, what is a modeling function? • Determine the slope of the function • Determine the y-intercept • Write in the form of y = mx + b

  9. Answer: Creating a Function from a Table • Determine slope by using

  10. Creating a Function from a Table • Now we know slope m = 3/2 • Use this and one ofthe points to determiney-intercept, b • Substitute an orderedpair into y = (3/2)x + b

  11. Creating a Function from a Table • Double check results • Substitute a different ordered pair into the formula • Should give a true statement

  12. Assignment • Lesson 2.1 • Page 71 • Exercises 1 – 35 odd

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