98 ­ Direct Variation.notebook
January 27, 2017
3
Table of Contents
18 ­ 19 Converting
20 ­ 21 Comparing
22 Proportion Review
23 Measurement Quiz
24 ­ 25 Direct Variation
Topic: • Algebra
LT/Focus: • I can identify direct variation in a
graph, table, or equation.
EQ: • What are the characteristics of direct
variation?
25
direct variation is a special
type of proportion
1
98 ­ Direct Variation.notebook
January 27, 2017
These graphs show
are the
Pull
direct variation:
cteristics of direct
tion on a graph?
These graphs do
NOT show direct
variation:
direct variation- graph is a
straight line through the origin
y = kx
2
98 ­ Direct Variation.notebook
January 27, 2017
• Algebra
LT/Focus: • I can identify direct variation in a
table or graph.
direct on
EQ: • What are the characteristics of
i
t
iat
ec
variation?
What is direct Two quantities x and y show ________ ar
dir _______
v when y = kx, variation?
where k is a number and k ≠ 0.
How do I know
if a graph shows
dir. var.?
1. All the points lie on a straight line.
2. The line passes through the origin.
Examples:
How do I know
if a table shows
dir. var.?
1. The data has a constant rate of change.
Move to Next Slide
2. When x = 0, y = 0.
x y
x y
x y
0
1
2
3
How do I know
if an equation
shows dir. var.?
0
3
6
9
0 1
1 4
2 7
3 10
‐1
‐2
1
3
2
6
1. It can be written y= kx, when k ≠ 0.
2. The equation doesn't contain any adding or subtracting, just multiplying.
Examples:
1. y = 4x
2. y = 4x + 3
3. 2y = 4x
Is this a proportional relationship?
Proportional
Proportional
or
or
Not Proportional
Not Proportional
3
98 ­ Direct Variation.notebook
January 27, 2017
Is this a proportional relationship?
Proportional
Proportional
Not Proportional
Not Proportional
or
or
Is this a proportional relationship?
Proportional
Proportional
Not Proportional
Not Proportional
or
or
4
98 ­ Direct Variation.notebook
January 27, 2017
Learning Target:
• I can identify whether or not data in graph or a table
has a direct variation.
n
t
ec
io
iat
r
r
What is direct Two quantities x and y show ________ when y = kx, di _______
va
variation?
where k is a number and k ≠ 0.
How do I know
if a graph shows
dir. var.?
1. All the points lie on a straight line.
2. The line passes through the origin.
Examples:
proportional
Not
(not through origin)
How do I know
if a table shows
dir. var.?
1. The data has a constant rate of change.
2. When x = 0, y = 0.
x y
x y
x y
0
1
2
3
How do I know
if an equation
shows dir. var.?
Examples:
Not
(curves)
0
3
6
9
0 1
1 4
2 7
3 10
‐1
‐2
1
3
2
6
1. It can be written y= kx, when k ≠ 0.
2. The equation doesn't contain any Move to next slide
adding or subtracting, just multiplying.
1. y = 4x
2. y = 4x + 3
3. 2y = 4x
How do I know if an equation shows a proportional relationship?
y=x+2
y = 4x
5
98 ­ Direct Variation.notebook
January 27, 2017
Learning Target:
• I can identify whether or not data in graph or a table
has a direct variation.
n
t
ec
iat
io
r
r
What is direct Two quantities x and y show ________ when y = kx, di _______
va
variation?
where k is a number and k ≠ 0.
How do I know
if a graph shows
dir. var.?
1. All the points lie on a line.
2. The line passes through the origin.
Examples:
proportional
Not
(not through origin)
How do I know
if a table shows
dir. var.?
1. The data has a constant rate of change.
2. When x = 0, y = 0.
x y
x y
x y
0
1
2
3
How do I know
if an equation
shows dir. var.?
Examples:
Not
(curves)
0
3
6
9
0 1
1 4
2 7
3 10
‐1
‐2
1
3
2
6
proportional
proportional
Not
not through (0, 0)
x 3 = y
x 2 = y
1. It can be written y= kx, when k ≠ 0.
2. The equation doesn't contain any adding or subtracting, just multiplying.
1. y = 4x
2. y = 4x + 3
3. 2y = 4x
6
98 ­ Direct Variation.notebook
No, does not pass through (0,0).
January 27, 2017
Yes, constant rate is times 4, so if I extend the table to x = 0, y would equal 0.
3
No, can't be written as y = kx
No, does not have a constant rate.
3
Yes, can be written as y=kx
No, can't be written as y = kx
3x = y
(there is adding)
7
98 ­ Direct Variation.notebook
January 27, 2017
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98 ­ Direct Variation.notebook
January 27, 2017
9