Question

use the slope formula to find the slope of the line that passes through the two given points. state whether the line is increasing, decreasing, horizontal, or vertical.
(6,9) and (7,5)
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the slope is m = \boxed{}. (type an integer or a simplified fraction.)
b. the slope is undefined.

Explanation:

Step1: Recall slope formula

The slope formula 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 \((x_1, y_1)=(6, 9)\) and \((x_2, y_2)=(7, 5)\).

Step3: Substitute into formula

Substitute values into the slope formula: \(m=\frac{5 - 9}{7 - 6}\).

Step4: Simplify numerator and denominator

Calculate numerator: \(5 - 9=-4\). Calculate denominator: \(7 - 6 = 1\). So \(m=\frac{-4}{1}=-4\).

Step5: Determine line type

Since the slope \(m=-4\) is negative, the line is decreasing.

Answer:

A. The slope is \(m = -4\). The line is decreasing.