To find the slope of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the slope formula:
[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given the points \((-3, 1)\) and \( (1, -2) \):
- \((x_1, y_1) = (-3, 1)\)
- \((x_2, y_2) = (1, -2)\)
Let's apply these values to the slope formula:
[tex]\[
\text{slope} = \frac{-2 - 1}{1 - (-3)}
\][/tex]
First, simplify the numerator and denominator separately:
[tex]\[
\text{numerator} = -2 - 1 = -3
\][/tex]
[tex]\[
\text{denominator} = 1 - (-3) = 1 + 3 = 4
\][/tex]
Now, divide the numerator by the denominator:
[tex]\[
\text{slope} = \frac{-3}{4} = -0.75
\][/tex]
Thus, the slope of the line containing the points \((-3, 1)\) and \((1, -2)\) is \(-\frac{3}{4}\).
The correct answer is [tex]\(C. -\frac{3}{4}\)[/tex].
