To determine the slope of the line represented on the graph, we can use the formula for slope, $m = \frac{\Delta y}{\Delta x}$, which is the change in $y$-coordinates divided by the change in $x$-coordinates between two points on the line.

Step-by-Step Solution:

1. Identify Two Points on the Line: From the graph, we can observe two points where the line crosses grid points:

   • Point 1: (0, 0) (the origin)
   • Point 2: (3, -1)

2. Calculate the Change in $y$ (Δy): $\Delta y = y_2 - y_1 = -1 - 0 = -1$

3. Calculate the Change in $x$ (Δx): $\Delta x = x_2 - x_1 = 3 - 0 = 3$

4. Calculate the Slope: $m = \frac{\Delta y}{\Delta x} = \frac{-1}{3} = -\frac{1}{3}$

Conclusion:

The slope of the line is $m = -\frac{1}{3}$.

Answer:

The correct answer is: $m = -\frac{1}{3}$

Would you like a further breakdown or have any questions?

Here are some related questions:

1. How is the slope formula derived?
2. What does a negative slope indicate about the direction of a line?
3. How would the slope change if the line was steeper?
4. What is the significance of the slope in real-life applications?
5. How can you find the y-intercept from this graph?

Tip: When finding the slope, always pick two clear points on the line for accurate calculation.