To find the slope of the line passing through points [tex]\(A(4, 5)\)[/tex] and [tex]\(B(9, 7)\)[/tex], we use the formula for the slope of a line passing through two points, which is:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, the coordinates of point [tex]\(A\)[/tex] are [tex]\((x_1, y_1) = (4, 5)\)[/tex], and the coordinates of point [tex]\(B\)[/tex] are [tex]\((x_2, y_2) = (9, 7)\)[/tex].
Substitute these coordinates into the slope formula:
[tex]\[
\text{slope} = \frac{7 - 5}{9 - 4}
\][/tex]
Simplify the numerator and denominator:
[tex]\[
\text{slope} = \frac{2}{5}
\][/tex]
Therefore, the slope of the line [tex]\(\overleftrightarrow{A B}\)[/tex] is [tex]\(\frac{2}{5}\)[/tex].
The correct answer is [tex]\(\boxed{\frac{2}{5}}\)[/tex].
