For each equation given below, name the dependent and independent variables.
`x=(5y+3)/2`

Answer

To determine the dependent and independent variables in the equation \( x = \frac{5y + 3}{2} \), we can follow these steps:

### Step 1: Understand the Variables
In any equation, the independent variable is the one that you can choose freely, while the dependent variable is the one that depends on the value of the independent variable.

### Step 2: Identify the Variables in the Equation
In the equation \( x = \frac{5y + 3}{2} \), we have two variables: \( x \) and \( y \).

### Step 3: Determine the Independent Variable
Let's analyze the equation. If we choose a value for \( y \), we can calculate the corresponding value of \( x \). For example:
- If \( y = 1 \), then \( x = \frac{5(1) + 3}{2} = \frac{8}{2} = 4 \).
- If \( y = 2 \), then \( x = \frac{5(2) + 3}{2} = \frac{13}{2} = 6.5 \).

From this, we can see that we can freely choose values for \( y \) without being restricted by \( x \).

### Step 4: Determine the Dependent Variable
Since the value of \( x \) changes based on the value of \( y \), we conclude that \( x \) depends on \( y \). Therefore, \( x \) is the dependent variable.

### Conclusion
- **Independent Variable**: \( y \)
- **Dependent Variable**: \( x \)