Explanation:

To find the regression line of \( y \) on \( x \) for the given data points \((-1, 1)\) and \((3, 2)\), follow these points:

- Calculate Slope (b): The slope \( b \) is given by \(\frac{(y_2 - y_1)}{(x_2 - x_1)} = \frac{(2 - 1)}{(3 + 1)} = \frac{1}{4}\).

- Point-Slope Form: Use the point-slope form of the line equation: \( y - y_1 = b(x - x_1) \). Substituting \((-1, 1)\), it becomes \( y - 1 = \frac{1}{4}(x + 1) \).

- Simplify: Rearrange to get: \( 4y - x - 5 = 0 \), which is rearranged to \( x - 4y + 5 = 0 \).

Let's review the options:

- Option 1: \( x - 4y + 5 = 0 \) This is the correct regression line equation.

- Option 2: \( 3x + 2y - 1 = 0 \) doesn't match our equation.

- Option 3: \( x + 4y + 1 = 0 \) is not correct.

- Option 4: \( 5x - 4y + 1 = 0 \) is not the equation from our calculation.