To find the equation of the line in standard form, we can start with the slope-intercept form of the line, which is given by the equation:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept. Given that the slope \( m = 0.5 \), we can substitute that into the equation:
\[ y = 0.5x + b \]
Next, we use the point (4, -2) to find \( b \). Substituting \( x = 4 \) and \( y = -2 \):
\[ -2 = 0.5(4) + b \]
Calculating \( 0.5(4) \):
\[ -2 = 2 + b \]
Now, solving for \( b \):
\[ b = -2 - 2 = -4 \]
So the equation of the line in slope-intercept form is:
\[ y = 0.5x - 4 \]
To convert this to standard form \( Ax + By = C \), we can rearrange it:
\[ 0.5x - y = 4 \]
Next, we can eliminate the decimal by multiplying the entire equation by 2:
\[ 2(0.5x) - 2y = 2(4) \] \[ x - 2y = 8 \]
This doesn't match any of the given options yet, so let's rewrite in a more standard form. Adding \( 2y \) to both sides gives us:
\[ x + 2y = 8 \]
Now we can rearrange it to match the form that is presented in the options. We can rewrite it as:
\[ -1/2x + y = -4 \]
This matches option D:
\[ D) -\frac{1}{2}x + y = -4 \]
To verify the form matches, if we add \(\frac{1}{2}x\) to both sides:
\[ y = \frac{1}{2}x - 4 \]
Thus, the equation you can choose as the answer which represents the line in standard form is option D) \(-\frac{1}{2}x + y = -4\).
Summarizing, the answer is:
D) -1/2x+y=-4