To find the equation of the perpendicular line at the point (4, 3) to the line \(y + 2x = 5\), we'll need to follow these steps:

1. Determine the slope of the given line.

2. Find the negative reciprocal of the slope to get the slope of the perpendicular line.

3. Use the point-slope form to write the equation of the perpendicular line.

Let's start with step 1:

The given line is in the form \(y + 2x = 5\). To find the slope, we'll rearrange the equation into slope-intercept form (\(y = mx + b\)):

\(y = -2x + 5\)

From this equation, we can see that the slope of the given line is -2.

Step 2:

The negative reciprocal of the slope -2 is \(\frac{1}{2}\). This will be the slope of the perpendicular line.

Step 3:

We'll use the point-slope form (\(y - y_1 = m(x - x_1)\)) to write the equation of the perpendicular line. We're given the point (4, 3) through which the perpendicular line passes:

\(y - 3 = \frac{1}{2}(x - 4)\)

Now, let's simplify this equation:

\(2(y - 3) = x - 4\)

\(2y - 6 = x - 4\)

Rearrange the equation to get the standard form:

\(2y - x = 2\)