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 Friday In your notebook, complete the last example from yesterday.

Enrollment at Howell Middle School South year Student enrollment 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

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 – ) 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.

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 y = -2.2x c). The slope of your line degrees per line degrees per kilometer kilometer

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

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

Linear Interpolation Using a line or its equation to approximate a value BETWEEN two known values Predict the height of the 3 ½ years. years height of tree At 3 ½ years the height of the tree would be approximately 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

Linear Extrapolation Using a line or its equation to approximate a value OUTSIDE the range of known values years height of tree Predict the height of the 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

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 – = = 3x 3 = 3 5 = x 0 = ½x = -4 (2)(-4) = ½x (2) -8 = x 0 = -0.5x = = -0.5x -0.5 = = x f(x) = ½x + 4 f(x) = -0.5x 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 is 1.5.

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.

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