To determine the slope of the line described by the equation [tex]\( y - 9 = -2(x - 8) \)[/tex], follow these steps:
1. Identify the form of the equation:
The given equation is in the point-slope form, which is expressed as:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line, and [tex]\(m\)[/tex] is the slope.
2. Compare with the point-slope form:
Given:
[tex]\[
y - 9 = -2(x - 8)
\][/tex]
We can match this with the point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex].
Here, [tex]\( y_1 = 9 \)[/tex] and [tex]\( x_1 = 8 \)[/tex], indicating the point [tex]\((8, 9)\)[/tex] lies on the line. The coefficient of [tex]\((x - x_1)\)[/tex] is [tex]\(-2\)[/tex].
3. Determine the slope [tex]\(m\)[/tex]:
In the equation [tex]\( y - 9 = -2(x - 8) \)[/tex], the slope [tex]\(m\)[/tex] is the multiplier of [tex]\((x - x_1)\)[/tex]. This coefficient directly represents the slope of the line.
Therefore, [tex]\( m = -2 \)[/tex].
4. Conclusion:
The slope of the line described by the equation [tex]\( y - 9 = -2(x - 8) \)[/tex] is [tex]\(-2\)[/tex].
Hence, the correct answer is:
[tex]\[
\boxed{-2}
\][/tex]
