To find the slope of the line that passes through the given points, we can use the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
We can choose any two points from the table. Let's use the first two points \((10, 6)\) and \((13, 21)\):
- \( x_1 = 10 \), \( y_1 = 6 \)
- \( x_2 = 13 \), \( y_2 = 21 \)
Now, we can plug these values into the slope formula:
\[ m = \frac{21 - 6}{13 - 10} = \frac{15}{3} = 5 \]
Let's confirm the slope using another pair of points. We'll use \((16, 36)\) and \((19, 51)\):
- \( x_1 = 16 \), \( y_1 = 36 \)
- \( x_2 = 19 \), \( y_2 = 51 \)
Calculating the slope:
\[ m = \frac{51 - 36}{19 - 16} = \frac{15}{3} = 5 \]
Since both pairs of points give us the same slope, we can conclude that the slope of the line is:
\[ \boxed{5} \]
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