In a direct variation, y=84 when x=28. Write a direct variation equation that shows the relationship between x and y.Write your answer as an equation with y first, followed by an equals sign.

Sure, let's solve this step by step.

1. In a direct variation, the relationship between $y$ and $x$ can be expressed as $y = kx$, where $k$ is the constant of variation.

2. We are given that $y = 84$ when $x = 28$. We can use this information to find the value of $k$.

3. Substitute $y = 84$ and $x = 28$ into the equation $y = kx$: $84 = k \cdot 28$

4. Solve for $k$ by dividing both sides of the equation by 28: $k = \frac{84}{28}$

5. Simplify the fraction: $k = 3$

6. Now that we have the value of $k$, we can write the direct variation equation. Substitute $k = 3$ back into the equation $y = kx$: $y = 3x$

So, the direct variation equation that shows the relationship between $x$ and $y$ is: $y = 3x$