Recursive-Explicit-Linear Equations

```Overview of Chapter 3
• Slope
• Y=mx+b
• Line of best fit
• Barbie Bungee
• Point-slope equation
• Systems of Equations
 Graphing
 Elimination
 Substitution
Recursive Explicit 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
•  = −1 +
• 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 0 = 2,  = −1 + 6
1. Find the explicit formula
2. Find 22 using the explicit
3. Find n such that  = 86
1.  = 6 + 2
slope
initial value
2. 22 = 6 22 + 2
22 = 134
3. 86=6n+2
n=14
You try!
• Given the recursion 0 = 5,  = −1 − 2
1. Find the explicit formula
2. Find 8 using the explicit
3. Find n such that  = −35
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: 1 = 17
Explicit:  = −2 + 17
= −1 − 2
Example 3
• Write an equation in the form y=a +bx of the line
the passes through the points of an arithmetic
sequence with 0 = 20 and a common
difference of -5.7.