Calculate Slope from 100-Degree Angle: Line Direction Analysis

Find the slope of a line that makes an angle of 100 degrees with the positive part of the xaxis, and indicate whether the line is ascending or descending.

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.