To find the slope of the line that passes through the points [tex]\((1, 7)\)[/tex] and [tex]\((10, 1)\)[/tex], we can use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\((x_1, y_1) = (1, 7)\)[/tex] and [tex]\((x_2, y_2) = (10, 1)\)[/tex].
1. Identify the coordinates:
[tex]\( (x_1, y_1) = (1, 7) \)[/tex]
[tex]\( (x_2, y_2) = (10, 1) \)[/tex]
2. Calculate the change in [tex]\(y\)[/tex] (rise):
[tex]\[
y_2 - y_1 = 1 - 7 = -6
\][/tex]
3. Calculate the change in [tex]\(x\)[/tex] (run):
[tex]\[
x_2 - x_1 = 10 - 1 = 9
\][/tex]
4. Plug the values from steps 2 and 3 into the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-6}{9} = -\frac{2}{3}
\][/tex]
So, the slope of the line that passes through the points [tex]\((1, 7)\)[/tex] and [tex]\((10, 1)\)[/tex] is:
[tex]\[
-\frac{2}{3}
\][/tex]
Therefore, the correct answer is:
[tex]\[
-\frac{2}{3}
\][/tex]
