To find the slope between the points [tex]\((1, -3)\)[/tex] and [tex]\((0, -1)\)[/tex] from the given set of points, we use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given:
- Point 1: [tex]\((1, -3)\)[/tex]
- Point 2: [tex]\((0, -1)\)[/tex]
Now, let's denote [tex]\((x_1, y_1) = (1, -3)\)[/tex] and [tex]\((x_2, y_2) = (0, -1)\)[/tex].
Substitute these values into the slope formula:
[tex]\[ \text{slope} = \frac{-1 - (-3)}{0 - 1} \][/tex]
First, simplify the numerator:
[tex]\[ -1 - (-3) = -1 + 3 = 2 \][/tex]
Next, simplify the denominator:
[tex]\[ 0 - 1 = -1 \][/tex]
Now, divide the numerator by the denominator:
[tex]\[ \text{slope} = \frac{2}{-1} = -2 \][/tex]
Therefore, the slope between the points [tex]\((1, -3)\)[/tex] and [tex]\((0, -1)\)[/tex] is [tex]\(-2\)[/tex]. Thus, the correct answer is:
[tex]\[
\boxed{-2}
\][/tex]
