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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

Slope

  • Y=mx+b
  • Line of best fit
  • Barbie Bungee
  • Point-slope equation
  • Systems of Equations
    • Graphing
    • Elimination
    • Substitution

Overview of Chapter 3

slide3
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.
slide8
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