To calculate the slope $m$, which represents the rate of change, we use the slope formula:

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

From the graph, the points provided are: $(x_1, y_1) = (2002, 77)$ and $(x_2, y_2) = (2006, 85)$.

Now substitute these values into the formula:

$m = \frac{85 - 77}{2006 - 2002} = \frac{8}{4} = 2$

The slope $m$ is 2, meaning the number of households with personal computers increased by 2 million per year.

Would you like a detailed explanation or have further questions? Here are 5 related questions for practice:

1. How would you interpret the slope in a real-world context?
2. What would the slope be if the increase was faster, say 12 million over 4 years?
3. How can you use this slope to predict the number of households in 2008?
4. What is the y-intercept in this situation, and how is it useful?
5. Can a negative slope occur in this context? Why or why not?

Tip: Always use labeled points from a graph carefully when calculating slope to ensure accuracy.