To find the slope of the line given by the equation [tex]\( x + 2y = 16 \)[/tex], we will convert this equation to the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\(m\)[/tex] represents the slope.
Here are the steps:
1. Start with the given equation:
[tex]\[
x + 2y = 16
\][/tex]
2. Isolate [tex]\( y \)[/tex] on one side of the equation. To do this, we first move the [tex]\( x \)[/tex] term to the right side by subtracting [tex]\( x \)[/tex] from both sides of the equation:
[tex]\[
2y = -x + 16
\][/tex]
3. Next, solve for [tex]\( y \)[/tex] by dividing every term by 2:
[tex]\[
y = \frac{-x + 16}{2}
\][/tex]
4. Simplify this equation to get it in slope-intercept form:
[tex]\[
y = -\frac{1}{2}x + 8
\][/tex]
In the slope-intercept form [tex]\( y = mx + b \)[/tex], the coefficient of [tex]\( x \)[/tex] (denoted by [tex]\( m \)[/tex]) is the slope of the line.
Thus, from the equation [tex]\( y = -\frac{1}{2}x + 8 \)[/tex], we can see that the slope [tex]\( m \)[/tex] is [tex]\(-0.5\)[/tex].
So, the slope of the line given by the equation [tex]\( x + 2y = 16 \)[/tex] is [tex]\(-0.5\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{-0.5}
\][/tex]
