The image shows a graph with a line passing through points on a coordinate plane. We need to determine the slope of the line.

To find the slope of a line, we use the formula: $\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

Step-by-Step Solution

1. Identify two points on the line: Observing the graph, it looks like the line passes through $(4, -2)$ and $(-4, 4)$.
2. Calculate $\Delta y$ and $\Delta x$:
   • $\Delta y = 4 - (-2) = 6$
   • $\Delta x = -4 - 4 = -8$
3. Find the slope: $\text{slope} = \frac{\Delta y}{\Delta x} = \frac{6}{-8} = -\frac{3}{4}$

Conclusion

The slope of the line is $-\frac{3}{4}$.

Would you like more details on the calculation steps or have any further questions?

Here are some additional questions you might explore:

1. What does a negative slope indicate about the direction of a line?
2. How would the slope change if the line were steeper?
3. What is the slope of a horizontal line, and why?
4. What is the slope of a vertical line, and why?
5. How can you find the y-intercept of a line from its graph?

Tip: To quickly check a slope on a graph, count the "rise" and "run" between two clear points on the line.