To determine the slope of the line given by the equation:
[tex]\[
y + 2 = -3(x - 5)
\][/tex]
we need to compare it to the point-slope form of a linear equation, which is:
[tex]\[
y - y_1 = m(x - x_1)
\][/tex]
In this form, [tex]\( m \)[/tex] represents the slope of the line, and [tex]\((x_1, y_1)\)[/tex] is a point on the line.
Looking at the given equation:
[tex]\[
y + 2 = -3(x - 5)
\][/tex]
we can see that it fits the point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex].
By comparing:
[tex]\[
y - y_1 = -3(x - x_1)
\][/tex]
to the given equation [tex]\( y + 2 = -3(x - 5) \)[/tex], we identify that the slope [tex]\( m \)[/tex] is given by the coefficient of [tex]\((x - x_1)\)[/tex], which is [tex]\(-3\)[/tex].
Therefore, the slope [tex]\( m \)[/tex] is:
[tex]\[
\boxed{-3}
\][/tex]
The correct answer is:
C. [tex]\(-3\)[/tex]
