Overview of chapter 3
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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. .

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Overview of Chapter 3

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Overview of chapter 3

  • 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

RecursiveExplicit Linear Equations

3.1


Overview of chapter 3

Goal

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


Remember when

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

Recursive

  • Find the next term by looking at the previous


Explicit

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

Linear

  • y=mx+b

  • m=slope

  • b=y-intercept

  • Linear uses x and y.


Overview of chapter 3

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

Example 1

  • Given the recursion

  • Find the explicit formula

  • Find using the explicit

  • Find n such that


Example 1 answers

Example 1: answers

slope initial value

2.

3. 86=6n+2

n=14


You try

You try!

  • Given the recursion

  • Find the explicit formula

  • Find using the explicit

  • Find n such that


Example 2

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

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.

  • Answer:

    -5.7=slope=b

    y=20-5.7x


Homework

Homework

  • 3.1

  • Problems: 1,4,5


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