Linear vs. Nonlinear
Jimmy is 50 miles from home and drives 20 miles per hour toward home.
Is this situation linear or nonlinear?
Linear (distance changes at a constant rate).
What makes a relation a function?
Each input has exactly one output.
What is slope-intercept form?
y=mx+b
Plan A table:
0 min → $30
2 min → $30.20
How much for 20 minutes?
Rate = $0.10 per minute
30 + (0.10 × 20) = 32
$32
Largest planet?
Jupiter
There are 2 water lilies on Day 1, 4 on Day 2, 8 on Day 3, and 16 on Day 4.
Is this situation linear or nonlinear?
Nonlinear (it doubles each day — exponential growth).
List the inputs and outputs for
{(−2, 3), (3, −2), (1, 3), (0, −2)}
Inputs: −2, 3, 1, 0
Outputs: 3, −2
5 cars → $1,700
6 cars → $1,940
What is the rate of change?
$240 per car
(1940 − 1700 = 240)
Plan B: c = 35 + 0.05m
Cost for 20 minutes?
35 + (0.05 × 20)
35 + 1 = 36
$36
Chemical symbol for gold?
Au
An investor puts $600 into an account and adds $100 per week.
Is this situation linear or nonlinear?
Linear (constant increase of $100 per week).
Is the relation above a function?
Yes. No input repeats with different outputs.
How well does Mr. Voldeck shred on the slopes?
A) Incredible
B) Radical
C) Gold Medal Champ
D) All of the above.
D
Difference between Plan A and Plan B at 20 minutes?
36 − 32 = 4
$4 (Plan B costs $4 more)
Who wrote The Diary of a Young Girl?
Anne Frank
A book has 650 pages and Billy reads 20 pages each night.
Is this situation linear or nonlinear?
Linear (pages decrease at a constant rate).
What tells you a mapping diagram is NOT a function?
An input maps to more than one output.
Ryan charges $15 per half-hour. Write the equation.
y = 15x
x: −2, 0, 2, 4
y: −12, −6, 0, 6
Slope = +3
When x = 0, y = −6
y = 3x − 6
quare root of 144?
12
The height of a ball thrown into the air follows the equation
y= −16t2 + 20t +5.
Is this situation linear or nonlinear?
Nonlinear (it contains a squared term).
Why does the vertical line test determine if a graph is a function?
If a vertical line hits the graph more than once, one input has multiple outputs.
Mail carrier: e = 3h + 200
Rate of change and initial value?
Rate of change = $3 per house
Initial value = $200
$200 is base pay, $3 per house delivered.
Framing graph question — what does slope and y-intercept represent?
Slope = cost per inch of frame
Y-intercept = starting/base cost before inches are added
First state to ratify the Constitution?
Delaware