The value of y is directly proportional to the value of x. When x = 2, y = 12. What is the value of y when x = 4?
Understand the Problem
The question is asking to find the value of y when x equals 4, given that y is directly proportional to x and that y equals 12 when x is 2. This can be solved using the formula for direct proportion.
Answer
$24$
Answer for screen readers
The value of $y$ when $x = 4$ is $24$.
Steps to Solve
- Set up the direct proportionality equation
Since $y$ is directly proportional to $x$, we can express this relationship with the equation: $$ y = kx $$ where $k$ is the constant of proportionality.
- Determine the value of k
We know that when $x = 2$, $y = 12$. Plug these values into the equation to find $k$: $$ 12 = k \cdot 2 $$ Dividing both sides by 2 gives: $$ k = \frac{12}{2} = 6 $$
- Use k to find y when x = 4
Now that we have $k = 6$, we can use it to find $y$ when $x = 4$: $$ y = 6 \cdot 4 $$ Calculating this gives: $$ y = 24 $$
The value of $y$ when $x = 4$ is $24$.
More Information
In this problem, we used the concept of direct proportionality, which means that as one quantity increases, the other quantity increases at a constant rate. Knowing one pair of values allowed us to find the constant of proportionality, which was then used to find the second value.
Tips
- Confusing direct proportionality with inverse proportionality. In direct proportion, both quantities increase together.
- Failing to correctly solve for $k$ by applying the values inappropriately.
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