To determine the slope of a line that contains the points \((-2, 2)\) and \((3, 4)\), we can use the slope formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Here, \((x_1, y_1)\) and \((x_2, y_2)\) represent the coordinates of the given points.
First, identify the coordinates:
[tex]\[ x_1 = -2, \quad y_1 = 2, \quad x_2 = 3, \quad y_2 = 4 \][/tex]
Now, substitute these values into the slope formula:
[tex]\[ m = \frac{4 - 2}{3 - (-2)} \][/tex]
Calculate the numerator and the denominator separately:
[tex]\[ 4 - 2 = 2 \][/tex]
[tex]\[ 3 - (-2) = 3 + 2 = 5 \][/tex]
Now, substitute these results back into the slope formula:
[tex]\[ m = \frac{2}{5} \][/tex]
Hence, the slope of the line containing the points \((-2, 2)\) and \((3, 4)\) is \(\frac{2}{5}\).
Therefore, the correct answer is:
C. [tex]\(\frac{2}{5}\)[/tex]
