To determine the slope of the line given by the equation [tex]\( x + 2y = 16 \)[/tex], we need to first convert this equation from its standard form to the slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] the y-intercept.
Here are the step-by-step transformations:
1. Start with the given standard form of the equation:
[tex]\[
x + 2y = 16
\][/tex]
2. Isolate the [tex]\( y \)[/tex]-term:
[tex]\[
2y = -x + 16
\][/tex]
3. Solve for [tex]\( y \)[/tex] by dividing every term by 2:
[tex]\[
y = \frac{-x}{2} + \frac{16}{2}
\][/tex]
[tex]\[
y = -\frac{1}{2}x + 8
\][/tex]
The equation now is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m = -\frac{1}{2} \)[/tex].
Thus, the slope of the line [tex]\( x + 2y = 16 \)[/tex] is [tex]\( -0.5 \)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{-0.5}
\][/tex]
