To find the equation of a line given a slope and a point, we can use the point-slope form of the equation of a line:
\[ y - y_1 = m(x - x_1) \]
where \(m\) is the slope, and \((x_1, y_1)\) is the given point. Here, the slope \(m = -\frac{1}{2}\) and the point is \((4, 6)\).
Plugging in the values, we have:
\[ y - 6 = -\frac{1}{2}(x - 4) \]
Next, we simplify the equation:
- Distribute the slope on the right side:
\[ y - 6 = -\frac{1}{2}x + 2 \]
- Add 6 to both sides:
\[ y = -\frac{1}{2}x + 8 \]
Now we have the equation in slope-intercept form (\(y = mx + b\)). To convert it to standard form \(Ax + By = C\), we rearrange the terms:
- Add \(\frac{1}{2}x\) to both sides:
\[ \frac{1}{2}x + y = 8 \]
- To eliminate the fraction, multiply the entire equation by 2:
\[ x + 2y = 16 \]
Now we have the equation in standard form. The final answer is:
\[ \boxed{x + 2y = 16} \]