3.1 Linear or Not Linear, that is the Question
linear relationship - a relationship . . .
with a constant rate of change
We can tell a relationship is linear if the table . . .
increases or decreases by the same amount
We can tell a relationship is linear if the graph . . .
is a line
We can tell a relationship is linear if the equation . . .
can be written in the form dv = cr x iv + bp
Graph the relationship between the length of the side of a square and its perimeter.
The relationship
between side length and
perimeter of a square.
Perimeter (in)
64
60
1
2
3
4
28
5
6
7
24
20
16
12
8
4
0
8
1 2 3 4 5 6 7 8
Length of side (in)
Pull
x y
56
52
48
44
40
36
32
Would th
between
square lo
Graph the relationship between the length of the side of a square and its area.
The relationship
between side length and
area of a square.
Area (in2)
64
60
x y
56
52
48
44
40
36
32
28
1
2
3
4
5
6
7
24
20
16
12
8
4
0
8
1 2 3 4 5 6 7 8
Length of side (in)
Compare the graphs/relationships
The relationship
between side length and
perimeter of a square.
64
60
1 4
2 8
3 12
4 16
36
32
28
5 20
6 24
7 28
24
20
16
12
8
4
8 32
1 2 3 4 5 6 7 8
Length of side (in)
Area (in2)
Perimeter (in)
64
60
x y
56
52
48
44
40
0
The relationship
between side length and
area of a square.
x y
56
52
48
44
40
36
32
28
1 1
2 4
3 9
4 16
5 25
6 36
7 49
8 64
24
20
16
12
8
4
0
1 2 3 4 5 6 7 8
Length of side (in)
Find the slope and equation of the line.
The relationship
between side length and
perimeter of a square.
Perimeter (in)
64
60
x y
1 4
2 8
3 12
4 16
56
52
48
44
40
36
32
5 20
6 24
7 28
8 32
28
24
20
16
12
8
4
0
What is the rate of change in the
graph?
When the length of the side
increases by 1, the perimeter
increases by:
What is the equation of the line?
y=
4
1 2 3 4 5 6 7 8
Length of side (in)
Nonlinear relationships
The relationship
between side length and
area of a square.
Area (in2)
64
60
56
52
48
44
40
36
32
28
+1
+1
+1
+1
+1
+1
+1
24
20
16
12
8
4
0
1 2 3 4 5 6 7 8
Length of side (in)
When the rate of change is not
constant,
x y
(for example as x increases by 1, y
1 1
2 4
3 9
+3 doesn't increase by a constant amount)
4 16
+5
+7
+9
5 25
+11
6 36
+13
7 49
+16
8 64
this is called a . . .
nonlinear
relationship
Linear Equations
Standard
form
y = 2x - 5
2x - 5y = 12
y = 4x + 9
3 x - 2y = -4
7
-3x + y = 11
5
y = 3x + 1
4
y = x - 12
5
1.
Pull
ax + by = c
2.
Pull
y = mx + b
3.
Pull
Slopeintercept
form
No exponents.
x and y cannot be multiplied
or divided together
x and y cannot be in the
denominator
Are these functions linear or non-linear?
linear
y = -3x - 4
6x = 2y - 8
x+y=8
2x + 3y = 14
y=x+4
non-linear
y = 5x3
y = 4x2 - 5
8 =x
y
linear examples:
x
0
1
2
3
y
0
7
14
21
y = -3x + 5
Non -linear examples:
x
0
1
2
3
y
0
1
4
9
y = 3x4 - x3 + 1
You choose:
Linear:
Non:
y = -x + 1
y = -6
y = x3 + 4x2 - 1
y = x2 - 3x + 1
y = 7x
Yay or Nay
seat students in semi circle facing
the smartboard, kinda like hot
potato; is the ex on the board
linear? Yay or Nay, then toss the
"potato" to your left, correct
answers stay up, wrong answers go
down.
Get examples!!
OAA examples of linear or Non-Linear Questions
1.
2.
1.
3.
5.
4.
Homework:
A.
List each example in the correct category: Linear or Non-linear
B.
C.
y = 2x + 1
y=3+2
x
H.
F.
y = x3 - 12
J.
I.
y=x
K.
y = x2 - 1
Linear Non-Linear
L.
Homework:
B.
List each example in the correct category: Linear or Non-linear
Linear
Non-Linear
C.
A.
F.
y=3+2
x
y = x3 - 12
y = 2x + 1
H.
J.
y=x
K.
I.
L.
y = x2 - 1