Do Now 12/3/09Do Now 12/3/09Take out HW from last night. Take out HW from last night. -- Text p. 328, #3-6, 8-12 evens, 16 & 17 (4 graphs)Text p. 328, #3-6, 8-12 evens, 16 & 17 (4 graphs)

Copy HW in planner.Copy HW in planner.- Text p. 338, #4-14 evens, 18 & 20 (3 graphs)Text p. 338, #4-14 evens, 18 & 20 (3 graphs)- ““Pop”-Quiz sections 5.5-5.7 FridayPop”-Quiz sections 5.5-5.7 Friday

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

0000 0101 0202

Enrollment at Howell Middle School SouthEnrollment at Howell Middle School South

0303 0404 0505 0606 0707 0808yearyear

Stu

dent

enr

ollm

ent

Stu

dent

enr

ollm

ent

900900

890890

880880

930930

920920

910910

950950

940940

00 11 22 33 44 55 66 77 88 99

880880 890890 895895 890890 900900 900900 910910 905905 920920 930930

0909

Years since 2000

Enrollment

Draw a line of fit for the scatter plot. Write an equation that models the 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.number of years since 2000 as a function student enrollment.

x-axisx-axis

Write an equation using two Write an equation using two points on the line. points on the line.

Use the points (4, 900) andUse the points (4, 900) and (6, 910). (6, 910).

910 – 900910 – 900 = = _10_10_ = 5_ = 5 6 – 4 26 – 4 2

Find the y-intercept. Find the y-intercept. Use (4, 900).Use (4, 900).

y = mx + by = mx + b

900 = 5(4) + b b = 880 900 = 5(4) + b b = 880

y = 5x + 880 y = 5x + 880

HomeworkHomework Text p. 328, #3-6, 8-12 evens, 16 & 17 Text p. 328, #3-6, 8-12 evens, 16 & 17

3) positive correlation3) positive correlation

4) relatively no correlation4) relatively no correlation

5) negative correlation5) negative correlation

6) 6)

y = 11.5x – 0.28y = 11.5x – 0.28

8) C8) C

10) The independent variable is 10) The independent variable is always x not y. y decreases as x always x not y. y decreases as x increases. increases.

12) 12)

Relatively no correlation. No, Relatively no correlation. No, because there is relatively no because there is relatively no correlation you can not write an correlation you can not write an equation.equation.

HomeworkHomework Text p. 328, #3-6, 8-12 evens, 16 & 17 Text p. 328, #3-6, 8-12 evens, 16 & 17

16) a).16) a).

b). Positive b). Positive

correlation; correlation; the larger the the larger the home home range size the larger range size the larger

the percent of pacing the percent of pacing time.time.

c). No; it is below the c). No; it is below the expected percent of expected percent of time spent pacing. time spent pacing.

17) a).17) a).

b). Sample answer; b). Sample answer;

y = -2.2x + 111y = -2.2x + 111

c). The slope of your c). The slope of your line. -2.2 degrees per line. -2.2 degrees per

kilometerkilometer

Objective Objective

SWBAT make predictions using best-fitting SWBAT make predictions using best-fitting lineslines

SWBAT find the zero of a functionSWBAT find the zero of a function

Section 5.7 “Predict with Linear Section 5.7 “Predict with Linear Models”Models”

line that most closely follows line that most closely follows the trend of the data.the trend of the data.

Best-Fitting LineBest-Fitting Line y

x

the process of finding the best- the process of finding the best- fitting line to model a set of data fitting line to model a set of data using technology.using technology.

Linear RegressionLinear Regression

Linear InterpolationLinear Interpolation

Using a line or its equation to approximate a value BETWEEN two known values.

11

22

33

44

00 11 22 33 44 55 66 77

Predict the height of the tree @ 3 ½ years.

years

heig

ht o

f tr

ee

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). Use the points (1, 1) and (5, 4).

1 – 41 – 4 = = _-3_-3_ = 3/4_ = 3/41 – 5 -41 – 5 -4

Find the y-intercept. Use (1, 1).Find the y-intercept. Use (1, 1).y = mx + by = mx + b1 = 3/4(1) + b b = 1/4 1 = 3/4(1) + b b = 1/4 y = 3/4x + 1/4 y = 3/4x + 1/4

Plug in 3.5 years for x.y = ¾(3.5) + 1/4 y = ¾(3.5) + 1/4 y = 2 7/8 feety = 2 7/8 feet

Linear ExtrapolationLinear Extrapolation

Using a line or its equation to approximate a value OUTSIDE the range of known values.

11

22

33

44

00 11 22 33 44 55 66 77years

heig

ht o

f tr

ee

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). Use the points (1, 1) and (5, 4).

1 – 41 – 4 = = _-3_-3_ = 3/4_ = 3/41 – 5 -41 – 5 -4

Find the y-intercept. Use (1, 1).Find the y-intercept. Use (1, 1).y = mx + by = mx + b1 = 3/4(1) + b b = 1/4 1 = 3/4(1) + b b = 1/4 y = 3/4x + 1/4 y = 3/4x + 1/4

Plug in 6 years for x.y = ¾(6) + 1/4 y = ¾(6) + 1/4 y = 4 ¾ y = 4 ¾

Zero of a FunctionZero 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.Find the zero of the functions.

f(x) = 3x – 15f(x) = 3x – 15

0 = 3x – 150 = 3x – 15

+15 = +15+15 = +15

15 = 3x15 = 3x3 = 33 = 3

5 = x5 = x

0 = ½x + 40 = ½x + 4-4 = -4-4 = -4

(2)(-4) = ½x (2)(2)(-4) = ½x (2)

-8 = x-8 = x

0 = -0.5x + 0.750 = -0.5x + 0.75-0.75 = -0.75-0.75 = -0.75

-0.75 = -0.5x-0.75 = -0.5x-0.5 = -0.5-0.5 = -0.5

1.5 = x1.5 = x

f(x) = ½x + 4f(x) = ½x + 4 f(x) = -0.5x + 0.75f(x) = -0.5x + 0.75

The zero off(x) = 3x -15 is 5.

The zero off(x) = 1/2x + 4 is -8.

The zero off(x) = -0.5x + 0.75 is 1.5.

Graphing Calculator ActivityGraphing Calculator Activity“Perform Linear Regression”“Perform Linear Regression”

Linear regression-Linear regression- the process of finding the the process of finding the best fitting line to model a set of data.best fitting line to model a set of data.

Using a graphing calculator, read and Using a graphing calculator, read and complete examples 1 & 2 in the text on complete examples 1 & 2 in the text on page 332 & 333. Then complete the page 332 & 333. Then complete the PRACTICE problems #1-5. Write your PRACTICE problems #1-5. Write your answers on a new page in your notebook. answers on a new page in your notebook. Refer to page 325 for assistance. Refer to page 325 for assistance.

HomeworkHomework

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