To find the slope of the line that contains the points [tex]\((-5, -4)\)[/tex] and [tex]\((-3, -5)\)[/tex], we can use the slope formula. The slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, the coordinates of the points are:
[tex]\( (x_1, y_1) = (-5, -4) \)[/tex]
[tex]\( (x_2, y_2) = (-3, -5) \)[/tex]
Substituting these values into the slope formula:
[tex]\[ m = \frac{-5 - (-4)}{-3 - (-5)} \][/tex]
First, simplify the expressions inside the parentheses:
[tex]\[ m = \frac{-5 + 4}{-3 + 5} \][/tex]
Next, perform the arithmetic operations in the numerator and the denominator:
[tex]\[ m = \frac{-1}{2} \][/tex]
Thus, the slope of the line that contains the points [tex]\((-5, -4)\)[/tex] and [tex]\((-3, -5)\)[/tex] is:
[tex]\[ m = -\frac{1}{2} \][/tex]
Therefore, the correct answer is:
[tex]\[
-\frac{1}{2}
\][/tex]
