1. Do Now 12/3/09 Take out HW from last night. -Text p. 328, #3-6, 8-12 evens, 16 & 17 (4 graphs) Copy HW in planner. - Text p. 338, #4-14 evens, 18 & 20 (3 graphs) - “Pop”-Quiz sections 5.5-5.7 Friday In your notebook, complete the last example from yesterday.

2. 000102 Enrollment at Howell Middle School South 030405060708 year Student enrollment 900 890 880 930 920 910 950 940 0123456789 880890895890900900910905920930 09 Years since 2000 Enrollment Draw a line of fit for the scatter plot. Write an equation that models the number of years since 2000 as a function student enrollment. x-axis Write an equation using two points on the line. Use the points (4, 900) and (6, 910). 910 – 900 = _10_ = 5 6 – 4 2 Find the y-intercept. Use (4, 900). y = mx + b 900 = 5(4) + b b = 880 y = 5x + 880

3. Homework Text p. 328, #3-6, 8-12 evens, 16 & 17 3) positive correlation 3) positive correlation 4) relatively no correlation 4) relatively no correlation 5) negative correlation 5) negative correlation 6) 6) y = 11.5x – 0.28 y = 11.5x – 0.28 8) C 8) C 10) The independent variable is always x not y. y decreases as x increases. 10) The independent variable is always x not y. y decreases as x increases. 12) 12) Relatively no correlation. No, because there is relatively no correlation you can not write an equation.

4. Homework Text p. 328, #3-6, 8-12 evens, 16 & 17 16) a). 16) a). b). Positive correlation; the larger the home range size the larger the percent of pacing time. c). No; it is below the expected percent of time spent pacing. 17) a). 17) a). b). Sample answer; y = -2.2x + 111 y = -2.2x + 111 c). The slope of your line. -2.2 degrees per line. -2.2 degrees per kilometer kilometer

5. Objective SWBAT make predictions using best-fitting lines SWBAT make predictions using best-fitting lines SWBAT find the zero of a function SWBAT find the zero of a function

6. Section 5.7 “Predict with Linear Models” line that most closely follows the trend of the data. Best-Fitting Line y x the process of finding the best- fitting line to model a set of data using technology. Linear Regression

7. Linear Interpolation Using a line or its equation to approximate a value BETWEEN two known values. 1 2 3 4 01234567 Predict the height of the tree @ 3 ½ years. years height of tree At 3 ½ years the height of the tree would be approximately 2.875 feet tall. Find the equation of the best-fitting line. Use the points (1, 1) and (5, 4). 1 – 4 = _-3_ = 3/4 1 – 5 -4 Find the y-intercept. Use (1, 1). y = mx + b 1 = 3/4(1) + b b = 1/4 y = 3/4x + 1/4 Plug in 3.5 years for x. y = ¾(3.5) + 1/4 y = 2 7/8 feet

8. Linear Extrapolation Using a line or its equation to approximate a value OUTSIDE the range of known values. 1 2 3 4 01234567 years height of tree Predict the height of the tree @ 6 years. Find the equation of the best-fitting line. At 6 years the height of the tree would be approximately 4 ¾ feet tall. Use the points (1, 1) and (5, 4). 1 – 4 = _-3_ = 3/4 1 – 5 -4 Find the y-intercept. Use (1, 1). y = mx + b 1 = 3/4(1) + b b = 1/4 y = 3/4x + 1/4 Plug in 6 years for x. y = ¾(6) + 1/4 y = 4 ¾

9. Zero of a Function A zero of a function is an x-value for which f(x) = 0. Because f(x) is the same as y, and y = 0 along the x-axis of the coordinate plane, a zero of a function is an x-intercept of the function’s graph. Find the zero of the functions. f(x) = 3x – 15 0 = 3x – 15 +15 = +15 15 = 3x 3 = 3 5 = x 0 = ½x + 4 -4 = -4 (2)(-4) = ½x (2) -8 = x 0 = -0.5x + 0.75 -0.75 = -0.75 -0.75 = -0.5x -0.5 = -0.5 1.5 = x f(x) = ½x + 4 f(x) = -0.5x + 0.75 The zero of f(x) = 3x -15 is 5. The zero of f(x) = 1/2x + 4 is -8. The zero of f(x) = -0.5x + 0.75 is 1.5.

10. Graphing Calculator Activity “Perform Linear Regression” Linear regression- the process of finding the best fitting line to model a set of data. Using a graphing calculator, read and complete examples 1 & 2 in the text on page 332 & 333. Then complete the PRACTICE problems #1-5. Write your answers on a new page in your notebook. Refer to page 325 for assistance. Using a graphing calculator, read and complete examples 1 & 2 in the text on page 332 & 333. Then complete the PRACTICE problems #1-5. Write your answers on a new page in your notebook. Refer to page 325 for assistance.

11. Homework Text p. 338, #4-14 evens, 18 & 20 (3 graphs) Text p. 338, #4-14 evens, 18 & 20 (3 graphs)