1. IMP 1- 11/9 (P), 11/10 (W) Warm Up- simplify each expression 1 ) 2 (x – 3) 2) 2x + 5x + 5y + 6y + 3 3) 2(x + 6) 4) 3x + 4 + 4x – 10 5) 10 – 2(3 + 4)

2. DUE TODAY pg. 217… Previous Travelers Please get your work out and place on your desk.

3. Due Next Class pg. 221 Who Will Make It? Use graph paper and a ruler to make your graphs Read carefully. Write KNOW? WANT? for each question BRING GRAPH PAPER MISSING ASSIGNMENTS due by Nov. 13 (any assignment on report dated 11/5 or 6)

4. Objective - Students will be able to find rules from tables and graphs

5. Agenda Warm Up/ Announcements Scatter Plot Pre-test Debrief Out Numbered, pg. 211- 212 Finish Previous Travelers, pg. 217 – 218 Sublette’s Cutoff, pg. 220

6. Goals when creating a graph - graph accurately represents the data - graph is not misleading - graph is easy to read …not cluttered, or too small -scale is even, accurate and easy to read - labels (with units) and title are always included

7. Outnumbered Debrief Constant Rate Constant Rate- y value changes the same each time x increases by an even amount On a graph, a constant rate is indicated by a LINE

8. Outnumbered Debrief b = y-intercept y = mx + b b is the “beginning” or the value of y when x = 0 b is the “y- intercept” or the place where the graph of the line touches the y-axis

9. Finding rules from graphs….notes 1. Where does it begin? “b” 2. Is the middle increasing or decreasing? 3. By how much? m = rate of change m = slope m = how much does it change each time you add one to the x value? EQUATION y = mx + b (conventional) OR y = b ± mx

10. Basic graph terminology Label origin, (0, 0), x-axis, y-axis, line, quadrants I, II, III and IV, independent axis, dependent axis independent axis dependent axis x y line origin III III IV

11. more math code… We call the set of all points that fit a rule the “graph of the equation” The process of putting these points together to form an overall picture is called “graphing the equation”

12. pg. 213 debrief How is looking at a graph like looking at an in-out table? How can you tell from the table that the graph is not linear?? INOUT 39 416 525 636

13. pg. 213 debrief Although the inputs are changing by the same amount each step, the outputs are increasing by different amounts Take the first differences Take the second differences WHAT DO YOU NOTICE?

14. pg. 213 debrief CONSTANT CHANGE in the first differences with a regular change in the inputs results in a LINEAR GRAPH CONSTANT change in the SECOND differences with a regular change in the inputs results in a PARABOLA

15. pg. 213 debrief How can you tell from a table whether or not a graph will be a straight line? How can you tell from a table if a linear graph will go up or down from left to right?

16. pg. 217 - 218 Look at the table on pg. 218 HOW might you use the data about beans to plan for 20 people?

17. pg. 217 – 218 graph the data How do we set up our graph? 1) decide which variable is the independent variable and which is the dependent 2) consider min/ max values in data 3) read carefully to see what info is required 4) label and scale each axis 5) plot your points

18. pg. 218 Now plot the data points (x, y) is an ordered pair that gives us “directions” to place a point Start at the origin. Go right (+) or left (-) “x” units Go up (+) or down (-) “y” units THIS MARKS YOUR SPOT! Make a dot!

19. pg. 218 What does the upward trend of the data tell you? Is the change uniform?

20. pg. 218 Now draw a “line of best fit” Consider, should you start at the origin? Does that make sense in the context of your problem? Zero people need zero pounds of beans? YES!!! Start at (0, 0)

21. pg. 218 Based on the line of best fit, how many pounds of beans will EACH of your Overland Trail families need? Large family- 21 people Small family- 6 people Non- family- 7 people Conglomerate family- 8 people

22. pg. 218 Now find a rule for your LINE OF BEST FIT 1) make a NEW in/out table with points that spread out along the line- chose points that are on the “cross hairs” of the grid 2) write an algebraic rule for your line of best fit… Where does it begin? (b) Does the middle increase or decrease? By how much each time? (± m) MAKE SURE YOU DEFINE VARIABLES!!

23. pg. 218 Predict how many beans you will need for 21 people… 1) from your graph 2) using your equation

24. pg. 220 Sublette’s Cutoff 1) read the problem carefully SUMMARIZE the situation 2) write KNOW? WANT? 3) each student do # 1 – 4 on graph paper REMEMBER steps…. 4) be prepared to present your work