To determine the slope of the line that passes through the points [tex]\((-4, 2)\)[/tex] and [tex]\((8, 5)\)[/tex], we use the slope formula:
[tex]\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, [tex]\((x_1, y_1) = (-4, 2)\)[/tex] and [tex]\((x_2, y_2) = (8, 5)\)[/tex].
Plugging in these coordinates into the formula, we have:
[tex]\[
\text{slope} = \frac{5 - 2}{8 - (-4)}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
\text{slope} = \frac{3}{8 + 4}
\][/tex]
[tex]\[
\text{slope} = \frac{3}{12}
\][/tex]
Simplify the fraction:
[tex]\[
\text{slope} = \frac{1}{4}
\][/tex]
Therefore, the slope of the line that goes through the points [tex]\((-4,2)\)[/tex] and [tex]\((8,5)\)[/tex] is [tex]\(\frac{1}{4}\)[/tex].
Thus, the correct answer is:
C. [tex]\(\frac{1}{4}\)[/tex]
