# Linear Functions

## Linear Functions is FUN!

• Definitions
• Function Notation
• Interpreting Linear Functions Arising in Applications
• Analyzing Linear Functions
• Constructing and Comparing Linear Models
• Unit Reflection
• Cited Work

## Definitions

Rate- Ratio or fraction
Change- Difference or subtraction

EXAMPLE: 4x-2=2
Slope- Steepness of a line

EXAMPLE: A line going down the graph at 275 degrees
Rate of Change- Change of one quantity over the corresponding change in another.

Y-Intercept- The y value of the point where a line cross the y axis

X- intercept- The x value of the point where a line cross the x axis
Slope Formula- m= (y₂ - y₁)/(x₂ - x₁)
EX: m-(4₂-3₁)(5₂+1₁)

Slope Intercept Formula- y=mx+b Solving for y
EX: y=(4)(3)+2

Standard Formula- Ax+By=C
EX: 4x+5y=38

Point-Slope Formula- y - y₁ = m(x - x₁)
EX: 3 - 3₁ = m(5 - 5₁)

## System of Equations/Inequalities

The equations 3x+3y=57 and 4x+2y=58 represents the total balance from the drive through movie in two days. X represents the amount of adults and y represents the amount for children and seniors.

Constraints- x>0 The tickets may not be sold for \$0
y>0 The tickets may not be sold for \$0
Billy is marketing donuts and cookies to raise money for his books. The donuts costs \$2 and the cookies costs \$2. She needs at the least \$6. She later found out he will need more so he sold his action figures for \$4 and he lost \$6 he knows he will need to make \$12.

## Function Notations

This is an example of a function since the (x) input has exactly one (y) output.

And example #2 is not a function since the (x) input doesn't have one (y) output.
Tim was limited in his phone bill for \$0.30 for each minute he talked on the phone, and then a flat of \$10. The Function would be y=0.30x+10 and the function notation to model the linear function would be f(x)=0.30x+10
Recursive Formula: a(n)=a(n-1)+.3

## Interpreting Linear Functions Arising in Applications

Tim worked at his mothers show to save up to buy a video game. For each customer he helps he earns \$8. He already has \$20 in his wallet, find out how much money he could save with each customer he helps. F(x)=8x+20
y-Intercept=8 The amount if he helps 1 customer.
Slope(Rate of Change)= 8 since he is gaining his money saved.

## Analyzing Linear Functions

F(x)=0.7x+8
Tim heard about Bob's job and wanted to be like him. He searched for a job that paid \$2, but unlike Bob he had no money to begin with.
COMPARISON
The first example differs because it has a y-intercept of 14 and the other one doesn't. the other difference is that the slope for the first one is much steeper than the other one.

## Building Functions

Explicit Formula is a(sub n)=a(sub 1)+d(n-1) ; Plug d (common difference), n (term number), and a(sub 1)(the 1st term) values to find the sequence of the explicit formula.

Explicit- 3,6,9,12 find the 5th term d=3 n=3 a(sub 1)=3 a(sub 3)=3+3(3-1) So, the 5th term is 15

Recursive- 5,10,15,20 find the 5th term d=5 n=5 a(sub 5)=a(sub 5-1)+5 So, the 5th term is 25

## Constructing and Comparing Linear Models

Billy and Tim was racing. Since Billy was more in shape, he gave Tim 5 meters head start. If Billy runs 2m per second and Tim runs 1m per second, who will win the 50 m race?
Billy= red
Tim= blue

## Unit Reflection

This unit seemed very complex to me in ways I can not explain. I'm just glad its over. I know I didn't do my full benefits, but I know the next unit might be much better(not promising)