To find the slope of the line passing through the points given in the table, we can use the formula for the slope \( m \), which is defined as:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
We can choose any two points from the table to calculate the slope. Let's choose the points \( (4, 24) \) and \( (5, 19) \).
Here, we have:
- \( (x_1, y_1) = (4, 24) \)
- \( (x_2, y_2) = (5, 19) \)
Now substituting these values into the slope formula:
\[ m = \frac{19 - 24}{5 - 4} = \frac{-5}{1} = -5 \]
To confirm the slope is consistent, let's also use the next pair of points \( (5, 19) \) and \( (6, 14) \):
Here, we have:
- \( (x_1, y_1) = (5, 19) \)
- \( (x_2, y_2) = (6, 14) \)
Calculating the slope:
\[ m = \frac{14 - 19}{6 - 5} = \frac{-5}{1} = -5 \]
Now, let's check the points \( (6, 14) \) and \( (7, 9) \):
Here, we have:
- \( (x_1, y_1) = (6, 14) \)
- \( (x_2, y_2) = (7, 9) \)
Calculating again:
\[ m = \frac{9 - 14}{7 - 6} = \frac{-5}{1} = -5 \]
In all cases, the slope is consistently \( -5 \).
Thus, the slope of the line is
\[ \boxed{-5} \]