To find the slope of the line that passes through the points in the table, we can use the formula for the slope \( m \) between any two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's choose two points from the table, for example \((0, 2)\) and \((1, 7)\).
Here:
- \( (x_1, y_1) = (0, 2) \)
- \( (x_2, y_2) = (1, 7) \)
Now plug the values into the slope formula:
\[ m = \frac{7 - 2}{1 - 0} = \frac{5}{1} = 5 \]
To verify that this slope holds for other points in the table, we can check another pair, like \((1, 7)\) and \((3, 17)\).
Here:
- \( (x_1, y_1) = (1, 7) \)
- \( (x_2, y_2) = (3, 17) \)
So,
\[ m = \frac{17 - 7}{3 - 1} = \frac{10}{2} = 5 \]
Finally, let's verify with the points \((-4, -18)\) and \((0, 2)\):
Here:
- \( (x_1, y_1) = (-4, -18) \)
- \( (x_2, y_2) = (0, 2) \)
So,
\[ m = \frac{2 - (-18)}{0 - (-4)} = \frac{2 + 18}{0 + 4} = \frac{20}{4} = 5 \]
Since the slope is the same for all pairs of points we checked, we conclude that the slope of the line is:
\[ \boxed{5} \]