Answer: (6, 9)
Explanation:
We have the pairs:
x y
0 0
2 3
4 6
These can be written as points (0, 0), (2, 3) and (4, 6)
This seems to be a linear relationship:
A linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
In the cases where the point (0, 0) belongs to the graph, we have a proportional relationship, which is written as:
y = k*x
In this case we have that point, then this is a proportional relationship.
Now we could just replace the values of one of the points (not the (0,0) point) in the equation in order to find the value of x.
If we use the point (2, 3) we get:
y = 3
x = 2
then:
3 = k*2
3/2 = k
Then the relationship is:
y = (3/2)*x
Now we want to know the ordered pair such that x = 6, then we just eed to replace x by 6 in the above equation:
y = (3/2)*6 = 9
Then we have x = 6 and y = 9
The correct option is (6, 9)