The value of y is directly proportional to the value of x. When x = 5, y = 10. What is the value of y when x = 4?
Understand the Problem
The question is asking to determine the value of y when x equals 4, given that y is directly proportional to x. The relationship can be expressed mathematically using the proportionality constant derived from the provided values of x and y.
Answer
The value of $y$ when $x = 4$ is $8$.
Answer for screen readers
The value of $y$ when $x = 4$ is $8$.
Steps to Solve
- Determine the Proportionality Constant Given that $y$ is directly proportional to $x$, we can express this relationship as $y = kx$, where $k$ is the proportionality constant.
We know that when $x = 5$, $y = 10$. We can substitute these values to find $k$: $$ 10 = k(5) $$ Now, solve for $k$: $$ k = \frac{10}{5} = 2 $$
- Use the Proportionality Constant to Find $y$ at $x = 4$ Now that we have the constant $k = 2$, we can use it to find the value of $y$ when $x = 4$. Substitute $x = 4$ into the equation: $$ y = kx $$ Replace $k$ with 2: $$ y = 2(4) $$ Calculate $y$: $$ y = 8 $$
The value of $y$ when $x = 4$ is $8$.
More Information
In direct proportionality, as one quantity increases or decreases, the other does as well. The relationship can be represented as a straight line through the origin. Here, we used the known values to establish the constant of proportionality.
Tips
- Confusing direct proportionality with inverse proportionality. Always ensure the relationship is correctly identified as direct when using the equation $y = kx$.
- Neglecting to solve for the proportionality constant first can lead to errors in the final calculation.
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