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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

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

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.
- Answer:
-5.7=slope=b

y=20-5.7x

Homework

- 3.1
- Problems: 1,4,5