Using chips

R-2

Which one works and why? \
Student A:

2x+4+6x-5+7x+3=17x

-No add-ons or coins
-Just add numbers then x at the end



Student B:

2x+4+6x-5+7x+3=15x+2

-Added together. 2x+6x=7x=15x



**If x= 1, then both would be right. 

Questions:
If problems are the same, why 2 answers?
Where is the +2 from?


Rule:
Never assume x=
Don't mix apples and oranges (strips and the chips, bags and the coins, x and add-ons)
Always show the add-on Don't mix the constant or an add-on 

Generalyzing linear equations and Quiz

x (indep. variable) * constant + sometimes an add on= y (depend. variable)

y=mx+b

m=constant
b=add on
y=dependent variable
x=independent variable


When you see two letters  or a number and a letter next to each other, it means they are multiplied.


Representations:
1. Graph
2. Table
3. Equation

Can you show where the...
1. constant of probortinality
2. add-on
...is in a graph, table, and equation

Can you create some representations related to a word problem

TMWYK: About the intersecting y-axis

-related to the add on
-indep. variable (x) goes from + to -
-if it hits the y-axis at 0 - no add on
-where the first point is


** Add on is the y-intercept. It starts someplace other than zero on the y-axis.

The add on in a linear equation and t-shirt problem

TMWYK:
-Extra part
-Add or subtract
-Happens w/ head start/up front price
-When linear graphs don't start at the same place

***Where it hits or intersects the y-axis (ex. 45 in headstart) it starts at 0. Add on is 0.


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

Positive and negative constant of proportionality

 

Observations

-Goes down by 12 each time

-spend $12 each week

-money to time 

-Linear- consistent amount

 Rules

144- n x 12 = amount of $

-n x 12 + 144 = amount of $

12^2- n x 12

Graph

Starts at the top of the y-axis and goes down 

y is bigger than x

Positive and Negative Constant of Proportionality

      +                                                          -

n x constant                                  data pts go down

graph increases                            start at top of y-axis

indep and depen go up                -n x constant

                                                     week goes up (ind), $ goes down (dep)

L-55 Characteristics

Characteristics of a Linear:

Graph                                     Table                                        Equation
                                                                               *rule/equation can't change
                                                                               *find one of the axis in the equation
                                                                               *can create a graph from an equation
                                                                               *n x constant (what it goes up every time)
                                                                               *Goes up by each time (unit rate, constant of Prop)

Walkathon Plans

Walkathon

Plan A
$10 regardless of miles

Plan B
$2/ mile walked

Plan C
$5 regardless of miles plus $.50/ mile walked

Which plan would you make the most money for the least amount of miles?