We are asked to find the equation of a line that passes through the point $(-1, 3)$ and is perpendicular to the line $y = -\frac{1}{2}x + 4$.

1. Problem Description

We are asked to find the equation of a line that passes through the point $(-1, 3)$ and is perpendicular to the line $y = -\frac{1}{2}x + 4$.

2. Solution Steps

First, we need to find the slope of the line perpendicular to $y = -\frac{1}{2}x + 4$. The slope of this line is $-\frac{1}{2}$. The slope of a line perpendicular to this line is the negative reciprocal of $-\frac{1}{2}$, which is $2$.

So, the line we are looking for has a slope of $2$ and passes through the point $(-1, 3)$. We can use the point-slope form of a line to find the equation of the line:

$y - y_1 = m(x - x_1)$

where $m$ is the slope and $(x_1, y_1)$ is the point. In our case, $m = 2$ and $(x_1, y_1) = (-1, 3)$. Plugging these values into the point-slope form, we get:

$y - 3 = 2(x - (-1))$

$y - 3 = 2(x + 1)$

$y - 3 = 2x + 2$

$y = 2x + 2 + 3$

$y = 2x + 5$

3. Final Answer

The equation of the line is $y = 2x + 5$. The answer is D.