Questions: Find the slope of the line, if it is defined. Through (-10,-8) and (-1,3) Write the expression that can be used to find the slope.

Transcript text: Find the slope of the line, if it is defined. Through $(-10,-8)$ and $(-1,3)$ Write the expression that can be used to find the slope. $\square$

Solution

Solution Steps

To find the slope of a line through two points, use the formula for the slope $ m $ which is given by the difference in the y-coordinates divided by the difference in the x-coordinates. Specifically, for points $(x_1, y_1)$ and $(x_2, y_2)$, the slope $ m $ is calculated as $ m = \frac{y_2 - y_1}{x_2 - x_1} $.

Step 1: Identify the Points

We are given two points: $(-10, -8)$ and $(-1, 3)$.

Step 2: Use the Slope Formula

The formula for the slope $ m $ of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Step 3: Substitute the Values

Substitute the given points into the slope formula: \[ m = \frac{3 - (-8)}{-1 - (-10)} \]

Step 4: Simplify the Expression

Calculate the differences: \[ m = \frac{3 + 8}{-1 + 10} = \frac{11}{9} \]