Question

find the slope of the line passing through the given points. state whether the line is increasing, decreasing, horizontal, or vertical.
(-7,-9) and (-1,-7)

select the correct choice below and fill in any answer boxes present in your choice.
a. the slope of the line is \boxed{}. (type an integer or a simplified fraction.)
b. the slope of the line is undefined.

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify coordinates

Let \((x_1, y_1) = (-7, -9)\) and \((x_2, y_2) = (-1, -7)\).

Step3: Substitute into formula

\( m = \frac{-7 - (-9)}{-1 - (-7)} = \frac{-7 + 9}{-1 + 7} = \frac{2}{6} = \frac{1}{3} \).

Step4: Determine line type

Since slope \( \frac{1}{3} > 0 \), the line is increasing.

Answer:

A. The slope of the line is \(\frac{1}{3}\). The line is increasing.