What is the slope of the line containing [tex]$(-3, 1)$[/tex] and [tex]$(1, -2)$[/tex]?

A. [tex]$\frac{3}{4}$[/tex]

B. [tex]$\frac{4}{3}$[/tex]

C. [tex]$-\frac{3}{4}$[/tex]

D. [tex]$-\frac{4}{3}$[/tex]



Answer :

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].