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Objectives Graph data and use a trend line to make predictions. Understand how transformations affect the look of an absolute value graph. Scatter Plots Graphs that relate two different sets of data by plotting the data as ordered pairs. Used to determine the relationship between data sets (for example, x and y values). Trend line: a line that approximates the relationship between the data sets of a scatter plot. Used to make predictions. Trend Lines by Hand Graph the set of data. Decide whether a linear model is reasonable. If so, draw a trend line and write its equation by hand. Then use a graphing utility to determine the equation of the trend line. {(1, 2), (3, 3), (3, 3.75), (4, 4), (5, 3.25), (6, 4.5)} 1. Place the ruler in such a way that half of the points are above the line and half of the points are below. 2. Draw the line 3. Write an equation for the line using two points This is much less accurate than calculator! Trend Lines on a Calculator Use a calculator to graph the set of data. Decide whether a linear model is reasonable. If so, make a trend line and find its equation. {(1, 2), (3, 3), (3, 3.75), (4, 4), (5, 3.25), (6, 4.5)} 1. Turn plots on: - 2nd STAT PLOT - Select option 1 - Highlight the word “ON,” hit ENTER 2. Enter data into a list (L1 = x values, L2 = y values): - STAT option 1 (Edit) - Highlight the titles L1 and L2 and push CLEAR - Enter your data into each list 3. GRAPH - To show a reasonable domain and range hit ZOOM 9 Trend Lines on a Calculator cont. 4. Use the graph to determine if the data is linear. If so, find the equation of the trend line: - 2nd QUIT to be on a blank screen - STAT arrow over to CALC option 4 (LinReg) ENTER - Write down your equation y = ax + b 5. Graph the trend line: - Hit the Y= button. Clear all existing equations. - VARS option 5 (Statistics) EQ option 1 (RegEQ) - GRAPH (ZOOM 9) Trend Lines on a Calculator An art expert visited a gallery and jotted down her guesses for the selling price of five different paintings. Then she checked the actual prices. The data points represent the cost (guess, actual) in hundreds of dollars. {(1, 2), (3, 3), (3, 3.75), (4, 4), (5, 3.25), (6, 4.5)} 1. Will a linear model fit this data? 2. If so what is the equation of the trend line? 3. If the actual price of a 6th painting was $1600, what might have the art expert’s guess been? Homework #14: Pg 81 #8, 12, 13, 21 (one of these problems must be done by hand) Pg 91 #29-32 2.1 – 2.4 QUIZ DUE FRIDAY!!