To find the slope of the blue line, we need to identify two distinct points on the line and use the slope formula:

$\text{slope (m)} = \frac{y_2 - y_1}{x_2 - x_1}$

Step 1: Identify Two Points on the Line

From the graph, the blue line passes through two clear points:

1. Point 1: $(0, -2)$
2. Point 2: $(3, 1)$

Step 2: Apply the Slope Formula

Using these two points $(x_1, y_1) = (0, -2)$ and $(x_2, y_2) = (3, 1)$: $\text{slope (m)} = \frac{1 - (-2)}{3 - 0} = \frac{1 + 2}{3} = \frac{3}{3} = 1$

Answer:

The slope of the blue line is 1. However, none of the answer choices directly match this slope, suggesting a possible misinterpretation or mistake in the answer options. Double-checking, none of the options given are correct if the slope is indeed 1.

Would you like further clarification or more details?

Here are some related questions to deepen understanding:

1. What are different methods to calculate slope if exact points are not clear on the graph?
2. How does the slope of a line change if it is rotated around the origin?
3. Why is the slope of a horizontal line always zero?
4. How can we determine the slope of a vertical line, and why is it undefined?
5. How do we find the equation of a line if we know its slope and one point?

Tip: When working with graphs, always verify the coordinates of points carefully to avoid errors in slope calculation.