To determine the slope of the line passing through two points, we use the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Given Points:

• $(0, 1)$
• $(3, -1)$

Step 1: Substituting values into the slope formula:

$m = \frac{-1 - 1}{3 - 0} = \frac{-2}{3}$

Final Answer:

The slope of the line is $\boxed{-\frac{2}{3}}$.

Would you like a step-by-step visual explanation of this process, or do you have further questions?

Here are 5 related questions to deepen your understanding:

1. How does changing the points on a line affect its slope?
2. What is the geometric meaning of a negative slope?
3. How can you determine the slope of a horizontal line?
4. How does the slope relate to the angle of a line with the x-axis?
5. How would the slope change if one of the points were reflected across the origin?

Tip: Always subtract the coordinates in the same order to avoid sign errors when calculating the slope.