# Linear Functions

### Brian Nguyen | December, 1 2015 | 3 Period

## Table of Contents

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

## Definitions

Change- Difference or subtraction

EXAMPLE: 4x-2=2

EXAMPLE: 4x-2=2

Slope- Steepness of a line

EXAMPLE: A line going down the graph at 275 degrees

EXAMPLE: A line going down the graph at 275 degrees

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

Constraints- x>0 The tickets may not be sold for $0

y>0 The tickets may not be sold for $0

## Function Notations

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.

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

__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- 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