To find the slope of the line that passes through the points \((-1, 2)\) and \( (3, 3) \), we can use the slope formula. The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's identify the coordinates given:
- \((x_1, y_1) = (-1, 2)\)
- \((x_2, y_2) = (3, 3)\)
Substitute these coordinates into the slope formula:
[tex]\[ m = \frac{3 - 2}{3 - (-1)} \][/tex]
Simplify the expression in the numerator (top part) and the denominator (bottom part):
[tex]\[ m = \frac{1}{3 + 1} \][/tex]
[tex]\[ m = \frac{1}{4} \][/tex]
So, the slope of the line that contains the points \((-1, 2)\) and \((3, 3)\) is:
[tex]\[ m = \frac{1}{4} \][/tex]
Therefore, the correct answer is:
C. [tex]\(\frac{1}{4}\)[/tex]
