1. What does Linear Mean? Linear or Not? How do I know?
Coordinate Plane Review
Domain & Range
Independent & Dependent Variables
Linear Functions
What does Linear Mean?
Linear or Not? How do I know?
Students will need a copy of the Vocabulary Notes
Cain Oct ‘08

2. Coordinate Plane Review Domain & Range
What is the domain and range of:
this table?
this relation?
{(-3,0),(1,4),(5,9)} x y -1 3 2 6 4 9 7
Domain: {-1,3,6,9}
Domain: {-3,1,5}
Range: {0,2,4,7}
Range: {0,4,9}

3. Coordinate Plane Review Domain & Range
What is the domain and range of a graph?
Domain is the x-value
What’s the smallest value of x?
Remember Compound Inequalities? 15
What’s the largest value of x? 10 4
Domain: 0 ≤ x ≤ 4
Write the domain as a compound inequality 5
Range is the y-value
What’s the smallest value of y? 15 5
What’s the largest value of y? 1 2 3 4
Write the range as a compound inequality
Range: 5 ≤ y ≤ 15

4. Independent & Dependent Variables
What is the domain and range of this graph?
Range: 15 ≤ r ≤ 54
Domain: 1 ≤ d ≤ 6
Range dependent
What’s the smallest and largest value of y?
largest value of x
smallest value of x
Domain independent variable

5. Independent & Dependent Variables
How do you determine independent and dependent variable?
What's x?
What's y?
Bowling costs $1.50 per game. I’m going bowling; how much will it cost?
2 variables are: # of games bowled and cost
__________ depends on ______________
cost
# of games bowled
Dependent
Independent y x

6. BREAK
for U3W3

7. Linear functions are lines
Linear functions have equal ratios of the changes in y-values to the changes in x-values.
Linear functions are lines
y-values
range
dependent variable
( expression in tables)
x-values
domain
independent variable
(variable)

8. Linear Functions
Linear functions have equal ratios of the changes in y-values to the changes in x-values.
With given points: Check from point to point, calculating the ratio of y-differences to x-differences.
This is Linear!
0-1=-1
-1-0=-1
Ratios
ARE THE SAME!
(-2,-1)
(0,0)
(2,1)
-2-0=-2
Calculate ratios of the changes in y-values to the changes in x-values.
0-2=-2

9. Linear or Not? How do I know? Is this function linear?
Equal ratios of the changes in y-values to the changes in x-values = Linear
1-2=-1
2-3=-1
Is this function linear? x 1 2 3 4 y -5 -3 -2 -3 -1 -1
-5-(-3)=-2
-3-0=-3
Simplifies to 2
Simplifies to 3
NOT Equal Not Linear
Note the y and f(x)
This is not linear

10. Linear or Not? How do I know?
Equal ratios of the changes in y-values to the changes in x-values = Linear
1-4=-3
-5-(-2)=-3
Is this function linear?
-2-1=-3 x -5 -2 1 4
f(x) -1
All ratios are equal! Linear -1 -1 -1 -3 -3 -3
-2-(-1)=-1
0-1=-1
-1-0=-1
Note the y and f(x)
Simplifies to 1 3
This is linear