What is the meaning of equality?

TMWYK: about solving for x


-Write a proportion
-Finding a missing # in an equation or proportion
-comp test, last problem
-You can break it down
-Do problem backwards
-Can use PEMDAS
-Guess and check
-  2 =   1
   4       2
-equal the same thing, have the same value
-2+4=3+3

Equation

R and L 64 T-shirt problem

Walkathon T-shirt problem

Given these equations, what do you think the C and n could stand for? Could you make up a problem? 

Mighty T

C= 49 + n
C=cost
n=# of students 
49 to create a design (add on)


No-Shrink T

C=4.5n
C=cost
n=number of students 
No add on, hits 0 axis


R/L 63
Here is the dilemma. I have $120. Which place should I go to buy the maximum amount of t-shirts. 

-Need two ways to justify your thinking

TMWYK: About the add on

*extra in linear problems
*not indep. or depend variable
*Found when indep (x) variable=0
*Intersecting y-axis for add-on?
*Called y-intercept because its where the line or what your graphing crosses the y-axis.
-It's the first point in the string of data

*The add on is where the intercept is

Positive and Negative Constant of Proportionality

+                          
*Add on at lowest point
*Dependent variable goes up



-
* Add on at highest point
*Dependent variable goes down

Henri and Emile

L-57 The Walking Race

Henri (younger): 1 meter per second     gets a 45 meter start   (1.5 meters slower)
Emile (older): 2.5 meters per second  (1.5 meters faster)

We want Henri to win, but not so obvious
How long/far should the race be?

*Tied at 30 seconds or 75 meters
(Race needs to be less than 75 meters)

Other Representations
-Tables
-Graphs
-Equations
-Models
-Rules

Graph
Independent Variable- Seconds
Dependent Variable- Meters

Equations
Henri    1s + 45
Emile    2.5s+0

Weeks and Money

 

Make 2 of the most relevant observations from this table. 

How is this table the same or different from the previous tables we have seen? 

-Goes down

-at 0 it is 144

L-57

144-w(12)=$

Which is the independent variable? Which is the dependent variable? 

Independent-

Dependent-

Constant of proportionality- 12

The 144 add on thing: This is the starter for the problem, It's the base. 

-Could be the head start like emile and Henri

***The add on/start is at week 0 

Where can I see the add on in this graph? 

-The highest point of the line

-The starting point

How can I find the constant of proportionality on the graph? 

-Every time is goes down by 12. 

-If you start at one point you can count the amount of spaces you go down. (The spaces between the point)

-The furthest point on the x-axis 

L-58   

What is the same and different about linear relationships that have positive and negative constant of proportionality? 

Pledge Problems

Plan A- $10 regardless of miles


Plan B- $2 per mile


Plan C-$5 plus $.50 per mile


Which plan is better? Why? Give three justifications (graph, table, equation)


Equations-

Plan A- $10      

Plan B- 2x=n   (x=miles, n=$)

Plan C- Miles x .50= $


What characteristics will be in all linear equations?
 -a constant of proportionality (multiply it by the independent variable)
-An equations that works for everything in the pattern (pos, neg, even, odd)
- Dependent variable = (indep. variable) (constant of proportionality)
-Amount $= (miles walked) x (4)
-unit rate***

Class is not entirely firm on these ideas.

Linear vs. Non-Linear and homework

R-56
Make observations on rules and graphs

Linear vs. No-linear

Linear                          Non-Linear
Straight line                 have two separate rules
Either pos or neg         negatives
up by a constant          doesn't go up by the same amount
have n                          have n















***The pattern of change is the constant of proportionality. How much something is going up by or down by. 


Homework: 7b pg 16 #3-5, 20

Graphing Patterns

Graphing Patterns
-example: x # of figures, y net value
-If it keeps going at the same rate, it will be straight.
-You need points to show where the data is
-You can use the rate to find the distance in between
-x comes first