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 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]