### Constant of Proportionality

```Constant of Proportionality
Direct Variation – constant ratio
A direct variation is
represented by a
ratio or equation :
y
k
x
or
y  kx
k≠0
EX1) Determine if the table represents a direct variation. If so, state the
x
y
constant of proportionality
Step 1 Substitute values
1 2 3 4
for variables
Step 2 Simplify
3 6 9 12
y
x
3
1
6
2
9
3
12
4
K=
3
3
3
3
This is a direct variation because the ratios
are constant. The constant of
proportionality is 3.
EX2) Identify the constant of proportionality in the equation y=15x
where y = cost of concert tickets and x = number of concert tickets
y = 15 x
Explain the relationship.
Each concert ticket cost \$15.
y=kx
k = constant of proportionality
15 = constant of proportionality
\$
EX3) Refer to the graph. Is there a direct variation? Explain
8
7
6
5
4
3
2
1
0
There is not a direct variation.
The line does not go through
the origin.
0
1
2
pounds
3
notes
Date ____________
Constant of Proportionality
Direct Variation –
A direct variation is represented by a ratio or equation :
EX1) Determine if the table represents a direct variation.
x
y
Step 1
Step 2
EX2) Identify the constant of proportionality. Explain the relationship.
k=
y=
x=
y = 15 x
\$
EX3) Refer to the graph. Is there a direct variation? Explain
8
7
6
5
4
3
2
1
0
0
1
2
pounds
3
```