Calculate Slope from 100-Degree Angle: Line Direction Analysis

To solve this problem, we'll follow these steps:

• Step 1: Use the formula $m = \tan(\theta)$
• Step 2: Calculate $\tan(100^\circ)$
• Step 3: Determine if the line is ascending or descending based on the slope

Now, let's work through each step:

Step 1: We use the formula for the slope of a line:
$\displaystyle m = \tan(\theta)$

Step 2: Substitute $\theta = 100^\circ$ into the formula:
$\displaystyle m = \tan(100^\circ)$

Using a calculator, $\tan(100^\circ) \approx -5.67$.

Step 3: Since the slope is negative, the line is descending.

Therefore, the solution to the problem is: $m = -5.67$, decreasing.