Questions: What is the slope of the line that passes through the Points (-9,-5) and (-1,-9)? Write your answer in simplest form.

Transcript text: What is the slope of the line that passes through the Points $(-9,-5)$ and $(-1,-9)$ ? write your answer in simplest form

Solution

Solution Steps

To find the slope of a line passing through two points, use the slope formula: $ m = \frac{y_2 - y_1}{x_2 - x_1} $. Substitute the given points $(-9, -5)$ and $(-1, -9)$ into the formula to calculate the slope.

Step 1: Identify the Points

The points given are $ P_1(-9, -5) $ and $ P_2(-1, -9) $.

Step 2: Apply the Slope Formula

The slope $ m $ of the line passing through the points $ P_1 $ and $ P_2 $ is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates of the points: \[ m = \frac{-9 - (-5)}{-1 - (-9)} = \frac{-9 + 5}{-1 + 9} = \frac{-4}{8} \]

Step 3: Simplify the Slope

Simplifying the fraction: \[ m = \frac{-4}{8} = -\frac{1}{2} \]