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# Overview of Chapter 3 PowerPoint PPT Presentation

Slope Y= mx+b Line of best fit Barbie Bungee Point-slope equation Systems of Equations Graphing Elimination Substitution . Overview of Chapter 3. Recursive Explicit Linear Equations. 3.1. Goal. Given one form if a linear equation, convert it to one of the other forms. .

Overview of Chapter 3

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#### Presentation Transcript

• Slope

• Y=mx+b

• Line of best fit

• Barbie Bungee

• Point-slope equation

• Systems of Equations

• Graphing

• Elimination

• Substitution

## RecursiveExplicit Linear Equations

3.1

### Goal

• Given one form if a linear equation, convert it to one of the other forms.

### Remember when….?

• What does the graph of an arithmetic sequence look like?

• We know there is another way calculate linear equations other than knowing the previous term right?

• Recursions are ONE type of equation. We will learn the other EQUIVALENT forms.

### Recursive

• Find the next term by looking at the previous

### Explicit

• b = Y-intercept. The initial value ( in the recursion.

• a= Slope (d in the recursion)

• Nice because you do not have to know the previous term to find the next.

### Linear

• y=mx+b

• m=slope

• b=y-intercept

• Linear uses x and y.

### So…

You will be given one of the three types just discussed, and will be asked to write it in a different way.

### Example 1

• Given the recursion

• Find the explicit formula

• Find using the explicit

• Find n such that

slope initial value

2.

3. 86=6n+2

n=14

### You try!

• Given the recursion

• Find the explicit formula

• Find using the explicit

• Find n such that

### Example 2

• You spend \$2 a day on lunch and have \$17 left after today.

Write a recursive and explicit formula modeling this situation.

So:

Recursive:

Explicit:

### Example 3

• Write an equation in the form y=a +bx of the line the passes through the points of an arithmetic sequence with and a common difference of -5.7.