Final answer:
To find y when x is 9 in a directly proportional relationship where y is 2 when x is 6, calculate the constant of proportionality (k), which is 1/3, and then multiply this by 9 to get y = 3.
Step-by-step explanation:
The question requires us to apply our knowledge of directly proportional relationships to find the value of y when x is 9, given that y is 2 when x is 6.
In directly proportional relationships, the ratio between the two quantities remains constant. As such, we can set up a proportion to find the unknown value.
To solve this, we first determine the constant of proportionality (k):
- y = k × x
- 2 = k × 6
- k = 2 / 6
- k = 1 / 3
Now we can use this constant to find y when x is 9:
Therefore, when x is 9, y is 3, demonstrating the proportionality between the two variables.