To find the slope, or rate of change, of the line containing the points [tex]\((6, -1)\)[/tex] and [tex]\((0, -7)\)[/tex], we use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, the coordinates of the two points are:
[tex]\[
(x_1, y_1) = (6, -1) \quad \text{and} \quad (x_2, y_2) = (0, -7)
\][/tex]
First, substitute the coordinates into the slope formula:
[tex]\[
\text{slope} = \frac{-7 - (-1)}{0 - 6}
\][/tex]
Simplify within the numerator and denominator:
Numerator:
[tex]\[
-7 - (-1) = -7 + 1 = -6
\][/tex]
Denominator:
[tex]\[
0 - 6 = -6
\][/tex]
Thus, the slope calculation becomes:
[tex]\[
\text{slope} = \frac{-6}{-6}
\][/tex]
Simplify the fraction:
[tex]\[
\frac{-6}{-6} = 1
\][/tex]
Hence, the slope (rate of change) of the line containing the points [tex]\((6, -1)\)[/tex] and [tex]\((0, -7)\)[/tex] is:
[tex]\[ \boxed{1} \][/tex]
