If y is directly proportional to x, and y = 24 when x = 2,what is the equation connecting y and x?

1. Break Down the Problem

To find the equation connecting $y$ and $x$, we need to establish the relationship where $y$ is directly proportional to $x$. This means that: $y = kx$ where $k$ is the constant of proportionality.

2. Relevant Concepts

Given:

• $y = 24$ when $x = 2$. We can use this information to find the value of $k$.

3. Analysis and Detail

1. Substitute the known values into the equation $y = kx$: $24 = k(2)$
2. Now, solve for $k$: $k = \frac{24}{2} = 12$

4. Verify and Summarize

We found $k = 12$. Therefore, the equation connecting $y$ and $x$ becomes: $y = 12x$ This means for any value of $x$, $y$ will be equal to $12$ times that value.

Final Answer

The equation connecting $y$ and $x$ is: $y = 12x$