where k is called the constant of proportionality, is a real number different than zero.
Here we have different tables, if for two pairs (x, y) of the table we have the same value of k, then the relation is proportional. Also you can see that if x = 0, we have:
y = k*0 = 0
then a proportional relationship always has the point (0, 0)
A)
X Y
1 6
2 12
3 18
Let's use the first two pairs:
(1, 6)
6 = k*1
6/1 = k = 6
(2, 12)
12 = k*2
12/2 = k = 6
in both cases we have k = 6, then this is a proportional relationship.
B)
X Y
2 0
4 2
6 4
Here we can see the pair (2, 0)
This means that when x = 2, we have y = 0
Then this can not be a proportional relationship, because:
0 = k*2
k = 0
This is not a proportional relationship.
C)
X Y
1 2
2 4
3 6
Let's find k for the first two points.
(1, 2)
2 = k*1
2/1 = k = 2
(2, 4)
4 = k*2
4/2 = k = 2
In both cases we have k = 2, then this is a proportional relationship.
D)
X Y
2 -4
4 -8
6 -12
Let's find k for the first two points:
(2, -4)
-4 = k*2
-4/2 = k = -2
(4, -8)
-8 = k*4
-8/4 = k = -2
In both cases we have k = -2, then this is a proportional relationship.
Vector components can form right triangle, since one acts vertically and the other acts horizontally. Thus, the original vector forms the hypotenuse of the right triangle formed by its components.
The process of breaking a vector down into its components is called vector resolution.
