To find the slope of the line that contains the points [tex]\((-5, -1)\)[/tex] and [tex]\((-9, 2)\)[/tex], you can use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, the coordinates of the points are:
- [tex]\( (x_1, y_1) = (-5, -1) \)[/tex]
- [tex]\( (x_2, y_2) = (-9, 2) \)[/tex]
Substitute these coordinates into the slope formula:
[tex]\[
m = \frac{2 - (-1)}{-9 - (-5)}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
m = \frac{2 + 1}{-9 + 5}
\][/tex]
[tex]\[
m = \frac{3}{-4}
\][/tex]
Therefore, the slope [tex]\(m\)[/tex] is:
[tex]\[
m = -\frac{3}{4}
\][/tex]
So, the correct answer is:
[tex]\[
-\frac{3}{4}
\][/tex]
