To find the slope of the line that passes through the points \((1, 7)\) and \((10, 1)\), we can use the formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, the coordinates of the points are:
- \((x_1, y_1) = (1, 7)\)
- \((x_2, y_2) = (10, 1)\)
Now, we can substitute the values into the slope formula:
\[ m = \frac{1 - 7}{10 - 1} \]
Calculating the values in the numerator and denominator:
\[ m = \frac{-6}{9} \]
Now simplify the fraction:
\[ m = -\frac{2}{3} \]
Thus, the slope of the line that passes through the points \((1, 7)\) and \((10, 1)\) is \(\boxed{-\frac{2}{3}}\).
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