To determine the slope ([tex]\(m\)[/tex]) of the line that passes through the points [tex]\((-1, -3)\)[/tex] and [tex]\((-2, 5)\)[/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]\((x_1, y_1) = (-1, -3)\)[/tex]
- [tex]\((x_2, y_2) = (-2, 5)\)[/tex]
Substitute the coordinates into the slope formula:
[tex]\[ m = \frac{5 - (-3)}{-2 - (-1)} \][/tex]
Simplify the numerator and the denominator:
[tex]\[ m = \frac{5 + 3}{-2 + 1} \][/tex]
[tex]\[ m = \frac{8}{-1} \][/tex]
Thus, the slope [tex]\(m\)[/tex] is:
[tex]\[ m = -8 \][/tex]
Looking at the choices given:
- None of these choices are correct.
- [tex]\(m = 8\)[/tex].
- [tex]\(m = -8\)[/tex].
- [tex]\(m = -4\)[/tex].
- [tex]\(m = 4\)[/tex].
The correct choice is:
[tex]\[ m = -8 \][/tex]
