Questions: Find the slope of the line that goes through the points (5,-14) and (11,-15). Slope, m= Enter your answer as an integer or a reduced fraction in the form A/B

$Find the slope of the line that goes through the points (5,-14) and (11,-15). Slope, m= Enter your answer as an integer or a reduced fraction in the form A/B$

Transcript text: Find the slope of the line that goes through the points $(5,-14)$ and $(11,-15)$. Slope, $m=$ $\square$ Enter your answer as an integer or a reduced fraction in the form A/B

Solution

Solution Steps

To find the slope of a line given two points, use the formula for the slope $ m $ which is the change in $ y $ divided by the change in $ x $. Specifically, for points $(x_1, y_1)$ and $(x_2, y_2)$, the slope $ m $ is calculated as $(y_2 - y_1) / (x_2 - x_1)$.

Step 1: Identify the Points

The two points given are $(5, -14)$ and $(11, -15)$.

Step 2: Apply the Slope Formula

The slope $ m $ of the line through the points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the values: \[ m = \frac{-15 - (-14)}{11 - 5} = \frac{-15 + 14}{6} = \frac{-1}{6} \]

Step 3: Simplify the Result

The slope simplifies to: \[ m = -\frac{1}{6} \]