To find the equation of the line in standard form, we can start from the slope-intercept form of a line, which is:
\[ y = mx + b \]
Here, \( m = -\frac{1}{2} \) (the slope) and we need to find the y-intercept \( b \). We know the line passes through the point (4, 6).
Substituting \( x = 4 \) and \( y = 6 \) into the slope-intercept equation:
\[ 6 = -\frac{1}{2}(4) + b \]
Calculating the value on the right:
\[ 6 = -2 + b \]
Adding 2 to both sides:
\[ b = 6 + 2 = 8 \]
Now we have the equation in slope-intercept form:
\[ y = -\frac{1}{2}x + 8 \]
Next, we will convert this equation to standard form, \( Ax + By = C \). To achieve this, we can eliminate the fraction by multiplying the entire equation by 2:
\[ 2y = -x + 16 \]
Now, rearranging this equation to standard form, we add \( x \) to both sides:
\[ x + 2y = 16 \]
Thus, the equation of the line in standard form is:
\[ x + 2y = 16 \]