How do we determine Linear, Line of Best Fit, and Inverse?

The students were given a variety of equations, word problems, graphs and tables. Their job was to determine if they are linear, line of best fit, inverse, or other.



The students solved the problems and then put them into groups.


First, they needed to sort out all of the linear problems.






Class put their Linears into categories...


Definitely Linear, Definitely not, still unsure




Class discovered that this (below) was linear instead of line of best fit.


-Look for slope
-Put points on graph and see if they are missing
-expand table

General Statements that cannot be linear

-exponent=not linear 

Which ones are line of best fit? 

Line of Best Fit

Inverse? Which problems were inverse?

R-51

If something is line of best fit, linear, or inverse what are some things to keep in mind?

What kind of clues tell me it is Linear?
-something goes up or down at a constant rate

What kind of clues tell me Line of Best fit?
-Somewhat scattered, but not random
-It has a linear trend

What kind of clues tell me Inverse?
- Constant w/ 2 variables
What are some things that will be on tomorrow's test?
-Put an equation in y=mx+b form
-Give an equation, graph, or a table and ask for the others (Including a word problem)
-Slope, x and y intercept
-parallel lines and/or perpendicular lines
-Given Line of Best fit data,will need to do general line, equation, and graph.
-Inverse: Ask for an equation

-Write equation when given:
   *graph
   *couple of points
   *table
   *Word Problem
   *Constant and 2 other variables (If there is a constant, it is inverse)

-Solve for x!!!!!!
-Great mathematical observations!
-Word Problems: Graphs, tables, equations
    *Linear, Line of Best Fit, Inverse

Middle School Science Field Trip

It costs 750 dollars to go on a science field trip.

A. It costs $3 per student if all kids go. Costs change depending on how many kids go.

B. It costs $5 per student no matter how many kids go.
     y=$ collected (total? )
     x=# of kids going

or

    y=cost/kid
    x=# of kids going 

What do we know?

Is it linear, inverse, or line of best fit?

Linear vs. Line of Best Fit vs. Inverse

L-45  Homework Due Friday 10/24

1. In an inverse relationship, can x ever be 0?



2. How is a negative slope different from an inverse relationship? 


L-46
pg. 69  #3-8, 27-30, 37

Inverse Relationship

The Cordova family is planning a trip of 300 miles to Mackinac Island, near the upper peninsula of Michigan.  Mr. Cordova does some calculations to see how the travel time will change if the family drives at different average speeds.

Date	Notes	Travel Time
February 15	Traveled by plane	1.5 hours
May 22	Drove	10 hours
July 3	Drove - stopped for repairs	14 hours
November 23	Flew - flight delayed	4 hours
December 23	Took overnight train	18 hours

We noticed:

As y gets bigger, x gets smaller

We are trying to decide an equation:

L x W=Area (First problem about the rectangle) L x W= 24

X + Y= coordinates

Travel Time x Coordinates

Maybe  one equation-multiple formats

Maybe multiple equations

We got this by using the X and Y variables to generalize them. ( for L x W could do X x Y= 24)

X x Y=Z

Now we have: 

X x Y= 24

x x y=500

What is Z? What is Z going to be for the inverse relationship? 

Class idea: x and y are variables and can change. Z is going to be constant that doesn't change.

We have x and y= some kind of a constant (class thinks it should be Z)

Class Strategies and Fast Food

Josh's Strategy


1. Found the avg. of the difference of the y-values
2.Divide by the change in the x values=slope
3. Expanded table using the slope to find the y-intercept


Emma's Strategy


1. Graphed Data
2. Graph a general line
      a. connect first-last point
      b. move all pts over a certain distance
3. Find the equation of general line




**Do you think there is a relationship between grams of fat and total calories in fast food?


-If there are more grams of fat, will there be more total calories?




Sandwich Type                                        Total Fat (g)      Total Calories                     
Hamburger                                                      9                      260
Cheeseburger                                                 13                     320
Quarter Pounder                                             21                    420
Quarter Pounder w/cheese                             30                     530
Big Mac                                                         31                     560
Special Sandwich                                          31                     550
Special Sandwich w/cheese & Bacon           34                     590       
Crispy Chicken                                              25                    500
Fish Filet                                                        28                    560
Grilled Chicken                                             20                    440
Grilled Chicken Lite                                       5                     300


What do you notice about this data? Math observations.
*Total calories all end in 0 (might influence how you scale the graph)
*More fat, more calories (w/ this noticing, would expect linear trend)
*A lot of the foods seem to be in the 500 calorie range (scale)
*Doesn't appear to be going up by a constant rate
*Special Sandwich w/ cheese and bacon has the most fat!
*Total Fat and Total calories doesn't seem to be in any order (May need to graph this)
* Add cheese and bacon, fat and calories go up
*Big Mac and Special Sandwich have same total fat, but different calories
*There are 2 dependent variables (Total Fat, Total Calories)
*Only graphing total fat and total calories, sandwich doesn't really matter


Where am I going to graph this?


x axis: Total fat (g)
y axis: Total calories

Review Quiz

The class reviewed this problem from the Quiz.



L-38


(2, -11)
(6,-9)


Some people had this as their slope:


1/2


-1/2




Where do you think they came up with that slope?


*Maybe people think it is supposed to be a neg because all the y's are neg
*Expanded table=-1/2 Maybe people got it because the x column is going down a 1/2

Hot chocolate!

Is the data linear?

Make an equation.

Where do we see linear relationships in the real world?

Where do we see linear relationships in the real world? 

Class ideas 

-wages and bank balance

-days and company profits 

-days and the stock marker value 

-speed and time 

-birthday and age 

-hearts rate per minute 

-gallons vs. total price 

-distance and time 

Linear relationships use a lot in the real world. Business world 

-profits

Look at the data. Do you think this data is linear or not? 

If it's linear, what does that mean? If it's not linear, what does that mean? 

Write data table on R page. Do work on L.