To find the slope of the line that passes through the given points [tex]\((-1, -4)\)[/tex], [tex]\( (0, -1)\)[/tex], [tex]\( (1, 2)\)[/tex], and [tex]\( (2, 5)\)[/tex], we can use the formula for the slope between any two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] on a line:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
We will use the first two points from the table to calculate the slope. The points are [tex]\((-1, -4)\)[/tex] and [tex]\( (0, -1)\)[/tex].
1. Identify the coordinates of the first point: [tex]\((-1, -4)\)[/tex]
[tex]\[
x_1 = -1, \quad y_1 = -4
\][/tex]
2. Identify the coordinates of the second point: [tex]\( (0, -1)\)[/tex]
[tex]\[
x_2 = 0, \quad y_2 = -1
\][/tex]
3. Substitute these values into the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-4)}{0 - (-1)}
\][/tex]
4. Simplify the expression:
[tex]\[
\text{slope} = \frac{-1 + 4}{0 + 1} = \frac{3}{1} = 3.0
\][/tex]
Therefore, the slope of the line passing through the given points is [tex]\( \boxed{3.0} \)[/tex].
