To find the slope of the line that passes through the points [tex]\((-4, -10)\)[/tex] and [tex]\((-7, -19)\)[/tex], we start by using the formula for the slope [tex]\(m\)[/tex] of a line when given two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, the coordinates of the points are:
- [tex]\((x_1, y_1) = (-4, -10)\)[/tex]
- [tex]\((x_2, y_2) = (-7, -19)\)[/tex]
We substitute the coordinates into the slope formula:
[tex]\[ m = \frac{-19 - (-10)}{-7 - (-4)} \][/tex]
This simplifies to:
[tex]\[ m = \frac{-19 + 10}{-7 + 4} \][/tex]
Continuing with the arithmetic:
[tex]\[ m = \frac{-9}{-3} \][/tex]
Finally, we simplify the fraction:
[tex]\[ m = 3 \][/tex]
Thus, the slope of the line that passes through the points [tex]\((-4, -10)\)[/tex] and [tex]\((-7, -19)\)[/tex] is [tex]\(\boxed{3}\)[/tex].
