To determine the slope of the line that passes through the points \((-3, 1)\) and \( (1, -2) \), we can use the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
where \((x_1, y_1) = (-3, 1)\) and \((x_2, y_2) = (1, -2)\).
Let's plug in the coordinates into the formula:
1. Calculate the difference in the y-coordinates (numerator):
[tex]\[
y_2 - y_1 = -2 - 1 = -3
\][/tex]
2. Calculate the difference in the x-coordinates (denominator):
[tex]\[
x_2 - x_1 = 1 - (-3) = 1 + 3 = 4
\][/tex]
3. Substitute these values into the slope formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3}{4}
\][/tex]
Thus, the slope of the line is:
[tex]\[
m = -\frac{3}{4}
\][/tex]
Comparing this with the provided answers:
- A. \(\frac{3}{4}\)
- B. \(\frac{4}{3}\)
- C. \(-\frac{3}{4}\)
- D. \(-\frac{4}{3}\)
The correct answer is:
[tex]\[ \boxed{-\frac{3}{4}} \][/tex]
