To find the slope of the line that passes through the points \((-1,2)\) and \((3,3)\), we use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here, \((x_1, y_1) = (-1, 2)\) and \((x_2, y_2) = (3, 3)\).
Substituting these values into the formula gives:
[tex]\[
m = \frac{3 - 2}{3 - (-1)}
\][/tex]
First, let's calculate the numerator (\(y_2 - y_1\)):
[tex]\[
3 - 2 = 1
\][/tex]
Next, calculate the denominator (\(x_2 - x_1\)):
[tex]\[
3 - (-1) = 3 + 1 = 4
\][/tex]
Now, divide the numerator by the denominator:
[tex]\[
m = \frac{1}{4}
\][/tex]
So, the slope of the line that contains the points \((-1, 2)\) and \((3, 3)\) is \(\frac{1}{4}\).
Therefore, the correct answer is:
C. [tex]\(\frac{1}{4}\)[/tex]
