IMP 1- 11/5 (P), 11/6 (W)• Warm up—complete the in/out table using substituting and

evaluatingex:y = 4(-2) - 4 = -8 – 4 = -12

What is the slope? the y-intercept?

x y = 4x - 4 -2 -12 -1 0 1 2 3

DUE TODAY “…pg. 246, #1, 2…”

Water Conservation

Students Presentput in left side of your group folder

Due Next ClassFINISH Previous Travelers, pg. 217 – 218

BRING GRAPH PAPER

MISSING ASSIGNMENTS due by Nov. 13 (any assignment on report dated 11/5 or 6)

Objective

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

AgendaWarm Up/ Announcements

From Rules to Graphs, pg. 213

Debrief Out Numbered, pg. 211- 212

Previous Travelers, pg. 217 - 218

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 and title are always included

pg. 213 From Rules to Graphs

We have gone from…. graph describing a situation graph finding a rule

Now we will go from… rule table graph

pg. 211- #1

1) How many people can one wagon hold?2) why does the rule Out = 8 · In make

sense?3) what does the 8 represent?4) use this number to tell me how many

people 100 wagons can hold.5) How many people would “w” wagons

hold?

pg. 211- 212 - # 2

1) how much coffee is consumed in 1 day? 2) how much coffee is there at the

beginning?3) does the amount increase or decrease?4) by how much each day?

pg. 212- #3

1) how much money is there in the cash register in the beginning?

2) does it increase or decrease?3) by how much for each additional

customer?

How do these numbers help us find the rule?

Outnumbered DebriefConstant Rate

• Constant Rate- as x increases by the same amount, the y variable changes the same amount each time

• On a graph, a constant rate is indicated by a LINE

Finding rules from graphs….notes1. Where does it begin? “b”2. Is it increasing or decreasing?3. By how much? m = rate of change m = slope m = how the middle changes EQUATION y = mx + b (conventional) OR y = b ± mx

Outnumbered Debriefb = y-intercept

• y = b ± mx b is the “beginning” or the value of y when x = 0 b is the “y- intercept” or the place where the graph touches the y-axis

Basic graph terminologySKETCH AND LABEL IN YOUR NOTES:

origin, (0, 0), x-axis, y-axis, line, quadrants I, II, III and IV, independent

axis, dependent axis

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”

math vocabulary…. …use the right words….

x- axis x- coordinate y- axis y- coordinate ordered pair coordinate system quadrant rate of change

pg. 216- 218 Previous Travelers

• read pg. 216 together as a classSUMMARIZE what we just read

read pg. 217 introductionSUMMARIZE what we just read

pg. 217

1. WANT?

KNOW? – data given on pg. 218

2. WANT? a) b) c)

pg. 217 - 218

• Look at the table on pg. 218• HOW might you use the data about beans

to plan for 20 people?

pg. 217 – 218graph the data

How do we set up our graph? 1) decide which variable is the independent

variable and which is the dependent? Which depends on the other? Does the pounds of beans needed depend on the

number of people?or the number of people depend on the pounds of

beans needed?

pg. 218

The “pounds of beans needed” depends on how many people there are so it is the dependent variable and is plotted on the y-axis (vertical like the tail of a y…..)

The “number of people” is the independent variable and is plotted on the horizontal or x-axis

pg. 218

• How should we scale the axis?

1) first, look at the minimum and maximum values. You need to have room for these

2) read the problem carefully. Do you need to make any predictions? Make sure your scale goes high enough to include the data points for your predictions as well!

pg. 218

Start both axes at ZERO. This is the norm, unless there is a good

reason to not start at zero!!

Starting at zero helps you find your rule!!Remember, b is the beginning, the y-

intercept– the y-value WHEN X = 0!!

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” unitsTHIS MARKS YOUR SPOT! Make a dot!

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)