1. Using Linear Models

2. A lot of situations can be modeled by a straight line… Example…Purchasing Gasoline. Gallons Purchased Total Cost 0$0 1$3.41 2$6.82 10$34.10

3. If we were to plot that data, what would it look like? GallonsTotal Cost 0$0 1$3.41 2$6.82 10$34.10 Perfectly Linear

4. How can we find the equation of that line? GallonsTotal Cost 0$0 1$3.41 2$6.82 10$34.10 Turn any two points into ordered pairs and then use the point-slope formula.

5. What does the slope indicate to you? What does the y-intercept mean to you? Based on the equation, how can you predict how many gallons you can get for $20?

6. Let’s do the Worksheet on Line of Best Fit together.

7. A lot of situations will not be modeled by a straight line… Example…A photography studio offers several packages to students posing for yearbook photos. Let x represent the number of pictures, and let y represent the price in dollars. Pictures, xPrice, y in $ 30$27 18$20 15$17 11$14

8. If we were to plot that data, what would it look like? PicturesPrice 30$27 18$20 15$17 11$14 No so Linear What can we do to find a linear model in this situation? 2 2

9. When the models are not perfectly linear, they are called scatter plots. In these instances, we determine a line of best fit or a regression line.

10. PicturesPrice 30$27 18$20 15$17 11$14 Envision a rectangular box drawn around the points. Draw a line through the center of the box leaning in the general direction of the points. Determine two points that your line has passed through (they may or may not be ordered pairs in your data table) 2 2 (10,14) (28,26) Now find the slope and the equation using either the point-slope formula or the slope-intercept formula. (Like we did yesterday).

11. Explain the real world meaning of the slope of the line. Explain the real world meaning of the y-intercept of the line. If the studio offers a 50-print package, what do you think it should charge? How many prints do you think the studio should include in the package for a $9.99 special?

12. Let’s do one more … The data below was collected from 9 students. Height,x in cmForearm, y in cm 185.948.5 172.044.5 155.041.0 191.550.5 162.043 164.342.5 177.547.0 180.048.0 179.547.5

13. Height,x in cm Forearm, y in cm 185.948.5 172.044.5 155.041.0 191.550.5 162.043 164.342.5 177.547.0 180.048.0 179.547.5 What is a good graphing window for your scatter plot? Let’s plot the data and draw the line of best fit.

14. Height,x in cm Forearm, y in cm 185.948.5 172.044.5 155.041.0 191.550.5 162.043 164.342.5 177.547.0 180.048.0 179.547.5 38 39 40 41 150 175 200

15. Write a linear equation that models the data. What does the calculator say is the line of best fit?

16. Explain the real world meaning of the slope of the line. Explain the real world meaning of the y-intercept of the line. Why doesn’t the real world meaning of the y-intercept make sense?

17. Use the equation to estimate the height of a student with a 50 cm forearm. Use the equation to estimate the length of a forearm of a student that is 158 cm tall.