To find the slope of the line passing through the points [tex]\((-2, 2)\)[/tex] and [tex]\((3, 4)\)[/tex], we use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the given points. Let's identify these values from our points:
- [tex]\(x_1 = -2\)[/tex]
- [tex]\(y_1 = 2\)[/tex]
- [tex]\(x_2 = 3\)[/tex]
- [tex]\(y_2 = 4\)[/tex]
Substituting these values into the slope formula:
[tex]\[ \text{slope} = \frac{4 - 2}{3 - (-2)} \][/tex]
Next, we simplify the expression step-by-step:
[tex]\[
\begin{align*}
\text{slope} & = \frac{4 - 2}{3 - (-2)} \\
& = \frac{2}{3 + 2} \\
& = \frac{2}{5}
\end{align*}
\][/tex]
Thus, the slope of the line is [tex]\(\frac{2}{5}\)[/tex]. Therefore, the correct answer is:
D. [tex]\(\frac{2}{5}\)[/tex]
