To determine the slope of the line described by the given equation, we need to rewrite the equation in the standard slope-intercept form of a linear equation, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope of the line and [tex]\( b \)[/tex] represents the y-intercept.
The given equation is:
[tex]\[ y - 5 = -3(x - 17) \][/tex]
This equation is already in the point-slope form, which is [tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( m \)[/tex] is the slope of the line, and [tex]\( (x_1, y_1) \)[/tex] is a point on the line.
From the equation:
[tex]\[ y - 5 = -3(x - 17) \][/tex]
It's clear that the coefficient of [tex]\((x - 17)\)[/tex] is the slope ([tex]\( m \)[/tex]). By comparing this with the point-slope form, we can directly see that the slope [tex]\( m \)[/tex] is [tex]\(-3\)[/tex].
Thus, the slope of the line described by the equation is:
[tex]\[ \boxed{-3} \][/tex]
Therefore, the correct answer is:
D. -3
