1. Students will be able to find a linear equation that approximates a set of data points. Warm-Up CD SINGLES The table shows the total number of CD single shipped (in millions) by manufacturers for several years during the period 1993–1997. Create a scatter plot of the data. Remember -x is the independent variable -y is the dependent variable

2. Students will be able to find a linear equation that approximates a set of data points. Homework Review

3. Students will be able to find a linear equation that approximates a set of data points. Quiz 5.1 – 5.4 When you are done with the quiz do not hand it in. I will collect it when everyone is done.

4. Students will be able to find a linear equation that approximates a set of data points. Warm Up Write an equation in slope-intercept form of the line that passes through the points. 1.(5, 32), (7,16) 2.(0, 160), (25, 610) 3. (-12, -15), (-18, -12) y = -8x + 72 y = 18x + 160 y = -1/2x - 21

5. Students will be able to find a linear equation that approximates a set of data points. Usually, there is no single line that passes through all the data points, so you try to find the line that best fits the data. This is called the best-fitting line. best-fitting line. There are several ways to find the best-fitting line for a given set of data points. In this lesson, you will use a graphical approach. –8 8 6 4 2 –2 –4 –6 0246–2–4–6–8 F ITTING A L INE TO D ATA

6. Students will be able to find a linear equation that approximates a set of data points. D ISCUS T HROWS Years since 1900 Distance (ft) 081624324048566472808896104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 Write an equation of your line. The winning Olympic discus throws from 1908 to 1996 are plotted in the graph. Approximate the best-fitting line for these throws.

7. Students will be able to find a linear equation that approximates a set of data points. Years since 1900 Distance (ft) 081624324048566472808896104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 S OLUTION Find two points that lie on the best-fitting line, such as ( 8, 138 ) and ( 96, 230 ). Find the slope of the line through these points. ( 96, 230 ). (96, 230) ( 8, 138 )

8. Students will be able to find a linear equation that approximates a set of data points. 92 88 = 1.05 Years since 1900 Distance (ft) 081624324048566472808896104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 (96, 230) (8, 138) y = m x + b 230 – 138 96 – 8 = 129.6 = b Write slope intercept form. Substitute 1.05 for m, 8 for x, 138 for y. Simplify. Solve for b. An equation of the best-fitting line is y = 1.05 x + 129.6. 138 = (1.05) (8) + b y = m x + b 138 = 8.4 + b y2 – y1y2 – y1 x2 – x1x2 – x1 m = In most years, the winner of the discus throw was able to throw the discus farther than the previous winner. 230 – 138 96 – 8 = 92 88 = 1.05

9. Students will be able to find a linear equation that approximates a set of data points. D ETERMINING THE C ORRELATION OF X AND Y In this scatter plot, x and y have a positive correlation, which means that the points can be approximated by a line with a positive slope.

10. Students will be able to find a linear equation that approximates a set of data points. D ETERMINING THE C ORRELATION OF X AND Y In this scatter plot, x and y have a negative correlation, which means that the points can be approximated by a line with a negative slope.

11. Students will be able to find a linear equation that approximates a set of data points. D ETERMINING THE C ORRELATION OF X AND Y In this scatter plot, x and y have relatively no correlation, which means that the points cannot be approximated by a line.

12. Students will be able to find a linear equation that approximates a set of data points. D ETERMINING THE C ORRELATION OF X AND Y T YPES OF C ORRELATION Positive Correlation No CorrelationNegative Correlation

13. Students will be able to find a linear equation that approximates a set of data points. Draw a scatter plot of the data. State the type of correlation that the data has. If possible, draw a line that closely fits the data and write an equation of the line. 1. 2. 3. XY 12 29 38 41 54 68 XY -38 -26 5 03 12 20 XY 1.15.1 1.75.5 2.25.9 2.66.3 3.37.5 3.57.6 No Correlation Negative Correlation Positive Correlation y = -1.54x + 3.23 y = 1.10x + 3.68

14. Students will be able to find a linear equation that approximates a set of data points. Practice: workbook 5-4