To find the slope of the line that passes through the points [tex]\((-2, 2)\)[/tex] and [tex]\( (3, 4)\)[/tex], we can use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the given points. In this case, [tex]\((x_1, y_1) = (-2, 2)\)[/tex] and [tex]\((x_2, y_2) = (3, 4)\)[/tex]. Substituting these values into the formula:
[tex]\[ m = \frac{4 - 2}{3 - (-2)} \][/tex]
First, simplify the numerator and the denominator:
[tex]\[ m = \frac{2}{3 + 2} \][/tex]
[tex]\[ m = \frac{2}{5} \][/tex]
Therefore, the slope of the line containing the points [tex]\((-2, 2)\)[/tex] and [tex]\((3, 4)\)[/tex] is
[tex]\[ \boxed{\frac{2}{5}} \][/tex]
So the correct answer is D. [tex]\( \frac{2}{5} \)[/tex].
