To find the slope of the line passing through the points [tex]\( A(4, 5) \)[/tex] and [tex]\( B(9, 7) \)[/tex], we use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, [tex]\( (x_1, y_1) = (4, 5) \)[/tex] and [tex]\( (x_2, y_2) = (9, 7) \)[/tex].
Substitute these coordinates into the slope formula:
[tex]\[ \text{slope} = \frac{7 - 5}{9 - 4} \][/tex]
Calculate the differences in the numerator and the denominator separately:
[tex]\[ y_2 - y_1 = 7 - 5 = 2 \][/tex]
[tex]\[ x_2 - x_1 = 9 - 4 = 5 \][/tex]
Now, divide the difference in the [tex]\( y \)[/tex]-coordinates by the difference in the [tex]\( x \)[/tex]-coordinates:
[tex]\[ \text{slope} = \frac{2}{5} \][/tex]
Therefore, the slope of [tex]\(\overrightarrow{AB}\)[/tex] is:
[tex]\[ \boxed{\frac{2}{5}} \][/tex]
