To find the slope \( m \) of the line that passes through the points \((x_1, y_1) = (1, 7)\) and \((x_2, y_2) = (10, 1)\), we can use the formula for the slope:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting in the coordinates of the points:
\[ m = \frac{1 - 7}{10 - 1} \]
Calculating the difference in the y-coordinates:
\[ 1 - 7 = -6 \]
And calculating the difference in the x-coordinates:
\[ 10 - 1 = 9 \]
Now, substituting these values back into the slope formula:
\[ m = \frac{-6}{9} \]
This can be simplified:
\[ m = \frac{-2}{3} \]
So, the slope of the line that passes through the points \((1, 7)\) and \((10, 1)\) is
\[ \boxed{-\frac{2}{3}}. \]
4 answers