To find the slope of the line that passes through the points in the table, we can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
We can choose any two points from the table. Let's use the first two points: \((4, -12)\) and \((16, -2)\).
Substituting these points into the formula, we have:
- \(x_1 = 4\)
- \(y_1 = -12\)
- \(x_2 = 16\)
- \(y_2 = -2\)
Now we can substitute into the slope formula:
\[ m = \frac{-2 - (-12)}{16 - 4} \] \[ m = \frac{-2 + 12}{12} \] \[ m = \frac{10}{12} \] \[ m = \frac{5}{6} \]
The slope of the line is \(\frac{5}{6}\).
To verify if this slope is consistent with the other pairs of points, we can also calculate the slope using the second pair \((16, -2)\) and \((28, 8)\):
- \(x_1 = 16\)
- \(y_1 = -2\)
- \(x_2 = 28\)
- \(y_2 = 8\)
Calculating the slope:
\[ m = \frac{8 - (-2)}{28 - 16} \] \[ m = \frac{8 + 2}{12} \] \[ m = \frac{10}{12} = \frac{5}{6} \]
Now using the pair \((28, 8)\) and \((40, 18)\):
- \(x_1 = 28\)
- \(y_1 = 8\)
- \(x_2 = 40\)
- \(y_2 = 18\)
Calculating the slope again:
\[ m = \frac{18 - 8}{40 - 28} \] \[ m = \frac{10}{12} = \frac{5}{6} \]
Since the slope calculated from all pairs is consistent, we confirm that the slope of the line is:
\[ \boxed{\frac{5}{6}} \]
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