The problem asks for the slope of the line shown in the graph. The slope of a line is calculated using the formula:

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

Where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

From the graph, two points that lie on the red line are:

• $(0, -2)$ (the y-intercept)
• $(4, 3)$

Now, we can substitute these points into the slope formula:

$m = \frac{3 - (-2)}{4 - 0} = \frac{3 + 2}{4} = \frac{5}{4}$

So, the slope $m$ is $\frac{5}{4}$.

Would you like a detailed explanation or further questions on this topic?

Here are five related questions to expand on this concept:

1. How do you find the slope if the line is vertical or horizontal?
2. What does a negative slope indicate about the direction of the line?
3. How would you calculate the slope if you were given the equation of a line?
4. Can you explain how to derive the slope-intercept form of a line from two points?
5. What is the significance of a slope of zero?

Tip: The slope can also be interpreted as the "rise over run," showing how much the line goes up (rise) or down (fall) as you move horizontally across the graph.