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 = 13?
Understand the Problem
The question asks for the value of y when x equals 13, given that y is directly proportional to x. The relationship can be expressed using the formula y = kx, where k is a constant. We need to find k using the provided values and then calculate y for x = 13.
Answer
The value of \(y\) when \(x = 13\) is $26$.
Answer for screen readers
The value of (y) when (x = 13) is (26).
Steps to Solve
- Identify the proportional relationship
Given that $y$ is directly proportional to $x$, we can express this relationship with the formula:
$$ y = kx $$
where $k$ is the constant of proportionality.
- Find the constant of proportionality (k)
From the problem, when $x = 3$, $y = 6$. We can substitute these values into the equation to find (k):
$$ 6 = k(3) $$
To solve for (k), we rearrange the equation:
$$ k = \frac{6}{3} = 2 $$
- Use the constant to find (y) when (x = 13)
Now that we know (k = 2), we can find (y) when (x = 13) using the original equation:
$$ y = kx = 2(13) $$
This simplifies to:
$$ y = 26 $$
The value of (y) when (x = 13) is (26).
More Information
In direct proportionality, as one variable increases, the other increases in a consistent ratio defined by the constant (k). Here, we calculated (k) using given values and applied it to find the desired value of (y).
Tips
- Confusing proportional relationships: Remember that direct proportionality means as one variable increases, the other increases linearly based on the constant (k).
- Incorrectly substituting values: Ensure you substitute the correct values into the equation when solving for (k) and (y).
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