Question

find the slope of the line passing through the pair of points or state that the slope is undefined. then indicate whether the line through the points rises, falls, is horizontal, or is vertical.
(-11,1) and (-6,-5)

select the correct choice below and, if necessary, fill in the answer box within your choice.

a. the slope is (simplify your answer. type an integer or a simplified fraction.)
b. the slope is undefined.
indicate whether the line through the points rises, falls, is horizontal, or is vertical.

a. the line rises from left to right.
b. the line is horizontal.
c. the line is vertical.
d. the line falls from left to right.

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( x_1=-11 \), \( y_1 = 1 \), \( x_2=-6 \), \( y_2=-5 \).

Step2: Substitute the values into the formula

Substitute the values into the slope formula: \( m=\frac{-5 - 1}{-6-(-11)} \).
Simplify the numerator and the denominator:
Numerator: \( -5 - 1=-6 \)
Denominator: \( -6 + 11 = 5 \)
So, \( m=\frac{-6}{5}=-\frac{6}{5} \).

Step3: Determine the direction of the line

Since the slope \( m =-\frac{6}{5}<0 \), the line falls from left to right.

Answer:

(for slope part):
A. The slope is \(-\frac{6}{5}\)