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 is asking to find the value of y when x is equal to 13, given that y is directly proportional to x. We need to use the relationship of direct proportionality to solve for y.
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
- Understand Direct Proportionality
Since $y$ is directly proportional to $x$, we can express this relationship mathematically as: $$ y = kx $$ where $k$ is the constant of proportionality.
- Find the Constant of Proportionality
From the given values, when $x = 3$, $y = 6$. We can substitute these values into the equation to find $k$: $$ 6 = k \cdot 3 $$ To solve for $k$, divide both sides by 3: $$ k = \frac{6}{3} = 2 $$
- Set Up the Equation for y
Now that we have $k$, we can rewrite the equation for $y$ as: $$ y = 2x $$
- Calculate y when x = 13
To find the value of $y$ when $x = 13$, substitute 13 into the equation: $$ y = 2 \cdot 13 $$ Calculate: $$ y = 26 $$
The value of $y$ when $x = 13$ is $26$.
More Information
In a directly proportional relationship, if one quantity increases, the other also increases at a constant rate defined by the proportionality constant. Here, the constant of proportionality was found to be 2.
Tips
- Misunderstanding Direct Proportionality: It's essential to recognize that direct proportionality means $y$ changes at a consistent rate relative to $x$.
- Calculation Errors: Ensure you correctly multiply or divide when finding the constant or calculating $y$.
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