Questions: Find the slope of the line passing through the points (9,-2) and (-1,-2) Then indicate whether the line through the points rises, falls, is horizontal, or is vertical.

Find the slope of the line passing through the points (9,-2) and (-1,-2) Then indicate whether the line through the points rises, falls, is horizontal, or is vertical.

Transcript text: Find the slope of the line passing through the points $(9,-2)$ and $(-1,-2)$ Then indicate whether the line through the points rises, falls, is horizontal, or is vertical.

Solution

Solution Steps

To find the slope of the line passing through two points, we use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points. After calculating the slope, we can determine the nature of the line based on the value of the slope.

Step 1: Calculate the Slope

To find the slope $ m $ of the line passing through the points $(9, -2)$ and $(-1, -2)$, we use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the given points: \[ m = \frac{-2 - (-2)}{-1 - 9} = \frac{0}{-10} = 0 \]

Step 2: Determine the Nature of the Line

Since the slope $ m = 0 $, the line is horizontal.