To determine the slope of the line that passes through the points [tex]\((-2, 2)\)[/tex] and [tex]\( (3, 4)\)[/tex], we will use the slope formula:
[tex]\[
m = \frac{y2 - y1}{x2 - x1}
\][/tex]
Here, [tex]\((x1, y1)\)[/tex] is [tex]\((-2, 2)\)[/tex] and [tex]\((x2, y2)\)[/tex] is [tex]\( (3, 4)\)[/tex]. Substituting these coordinates into the slope formula:
1. Calculate the numerator of the slope formula:
[tex]\[
y2 - y1 = 4 - 2 = 2
\][/tex]
2. Calculate the denominator of the slope formula:
[tex]\[
x2 - x1 = 3 - (-2) = 3 + 2 = 5
\][/tex]
3. Divide the numerator by the denominator to get the slope:
[tex]\[
m = \frac{2}{5}
\][/tex]
Thus, the slope of the line that passes through the points [tex]\((-2, 2)\)[/tex] and [tex]\( (3, 4)\)[/tex] is:
[tex]\[
m = \frac{2}{5}
\][/tex]
Therefore, the correct answer is:
A. [tex]\(\frac{2}{5}\)[/tex]
