To determine the slope of the line that contains the points [tex]\((-1, 2)\)[/tex] and [tex]\((3, 3)\)[/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 on the line.
Here, the coordinates of the points are:
[tex]\[
(x_1, y_1) = (-1, 2)
\][/tex]
[tex]\[
(x_2, y_2) = (3, 3)
\][/tex]
Substitute these values into the slope formula:
[tex]\[
\text{slope} = \frac{3 - 2}{3 - (-1)}
\][/tex]
Simplify the expressions in the numerator and the denominator:
[tex]\[
\text{slope} = \frac{1}{3 + 1}
\][/tex]
[tex]\[
\text{slope} = \frac{1}{4}
\][/tex]
Therefore, the slope of the line that contains the points [tex]\((-1, 2)\)[/tex] and [tex]\((3, 3)\)[/tex] is [tex]\(\frac{1}{4}\)[/tex].
The correct answer is:
B. [tex]\(\frac{1}{4}\)[/tex]
