To find the slope of the line passing through the points [tex]\((9, -5)\)[/tex] and [tex]\((1, -1)\)[/tex], we use the slope formula, which is given by:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] is the point [tex]\((9, -5)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is the point [tex]\((1, -1)\)[/tex]. Substituting these coordinates into the formula, we get:
[tex]\[
m = \frac{-1 - (-5)}{1 - 9}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
m = \frac{-1 + 5}{1 - 9}
\][/tex]
[tex]\[
m = \frac{4}{-8}
\][/tex]
Now, simplify the fraction:
[tex]\[
m = \frac{4}{-8} = -\frac{1}{2}
\][/tex]
Therefore, the slope of the line passing through the points [tex]\((9, -5)\)[/tex] and [tex]\((1, -1)\)[/tex] is:
[tex]\[
\boxed{-0.5}
\][/tex]
