The value of y is directly proportional to the value of x. When x = 3, y = 6. What is the value of y when x = 9?
Understand the Problem
The question is asking to find the value of y when x is given, under the condition that y is directly proportional to x. With the known values of x and y, we can establish a proportion to solve for the unknown y when x equals 9.
Answer
$y = 18$
Answer for screen readers
The value of $y$ when $x = 9$ is $y = 18$.
Steps to Solve
- Identify the Proportional Relationship
Since $y$ is directly proportional to $x$, we can express this relationship as: $$ y = kx $$ where $k$ is the constant of proportionality.
- Find the Constant of Proportionality
Using the known values $x = 3$ and $y = 6$, we can substitute to find $k$: $$ 6 = k \cdot 3 $$ To solve for $k$, divide both sides by 3: $$ k = \frac{6}{3} = 2 $$
- Substitute to Find $y$ When $x = 9$
Now that we have $k$, use the relationship to find $y$ when $x = 9$: $$ y = 2 \cdot 9 $$ Perform the multiplication: $$ y = 18 $$
The value of $y$ when $x = 9$ is $y = 18$.
More Information
This problem demonstrates the concept of direct variation, where one variable changes directly as another variable changes. In this case, when $x$ doubles, $y$ also doubles.
Tips
- Forgetting to establish the proportionality constant $k$ using given values.
- Misapplying the relationship by using incorrect values of $x$ and $y$.
