To determine the slope of the line described by the equation [tex]\( y - 9 = -2(x - 8) \)[/tex], we should recognize that this equation is written in point-slope form. The point-slope form of a line's equation is given by:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
In this format:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( (x_1, y_1) \)[/tex] is a point on the line.
Given the equation [tex]\( y - 9 = -2(x - 8) \)[/tex], we can directly identify the components:
- The slope [tex]\( m \)[/tex] is the coefficient of the [tex]\((x - x_1)\)[/tex] term, which in this equation is [tex]\(-2\)[/tex].
- [tex]\((x_1, y_1)\)[/tex] is the point [tex]\((8, 9)\)[/tex], but this is not required for determining the slope.
Thus, the slope [tex]\( m \)[/tex] of the line is [tex]\( -2 \)[/tex].
Hence, the correct answer is:
C. [tex]\(-2\)[/tex]
