To find the slope of the line passing through the points [tex]\((5, 2)\)[/tex] and [tex]\((8, 7)\)[/tex], we will use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] is the first point and [tex]\((x_2, y_2)\)[/tex] is the second point.
Given the points [tex]\((5, 2)\)[/tex] and [tex]\((8, 7)\)[/tex]:
[tex]\[
(x_1, y_1) = (5, 2) \\
(x_2, y_2) = (8, 7)
\][/tex]
Substitute these values into the slope formula:
[tex]\[
m = \frac{7 - 2}{8 - 5}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
m = \frac{5}{3}
\][/tex]
So, the slope of the line is:
[tex]\[
m = \frac{5}{3}
\][/tex]
Therefore, the correct choice is:
[tex]\[
\boxed{\frac{5}{3}}
\][/tex]
