To find the slope of the line given by the equation [tex]\(x + 2y = 16\)[/tex], we need to express this equation in the slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept.
Here are the steps to convert the given equation [tex]\(x + 2y = 16\)[/tex] into the slope-intercept form:
1. Start with the given equation:
[tex]\[ x + 2y = 16 \][/tex]
2. Isolate the term involving [tex]\(y\)[/tex] on one side of the equation. To do this, you need to subtract [tex]\(x\)[/tex] from both sides:
[tex]\[ 2y = 16 - x \][/tex]
3. Now, solve for [tex]\(y\)[/tex] by dividing every term by 2:
[tex]\[ y = \frac{16 - x}{2} \][/tex]
4. Simplify the right-hand side:
[tex]\[ y = \frac{16}{2} - \frac{x}{2} \][/tex]
[tex]\[ y = 8 - 0.5x \][/tex]
Now, the equation is in the slope-intercept form [tex]\(y = -0.5x + 8\)[/tex].
From this form, we can identify the slope [tex]\(m\)[/tex]:
[tex]\[ m = -0.5 \][/tex]
So, the slope of the line represented by the equation [tex]\(x + 2y = 16\)[/tex] is [tex]\(\boxed{-0.5}\)[/tex].
