To determine the slope of the line given by the equation [tex]\(x + 2y = 16\)[/tex], we need to rewrite the equation in slope-intercept form, which is [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] represents the slope.
Starting with the given equation:
[tex]\[ x + 2y = 16 \][/tex]
Our goal is to solve for [tex]\(y\)[/tex]. First, isolate the [tex]\(2y\)[/tex] term by subtracting [tex]\(x\)[/tex] from both sides:
[tex]\[ 2y = -x + 16 \][/tex]
Next, divide every term by 2 to solve for [tex]\(y\)[/tex]:
[tex]\[ y = -\frac{1}{2}x + 8 \][/tex]
Now, the equation is in slope-intercept form [tex]\(y = mx + b\)[/tex]. From the equation, we can see that the coefficient of [tex]\(x\)[/tex] is [tex]\(-\frac{1}{2}\)[/tex], which represents the slope [tex]\(m\)[/tex].
Therefore, the slope of the line [tex]\(x + 2y = 16\)[/tex] is:
[tex]\[ \boxed{-0.5} \][/tex]
