The image shows a graph plotting the number of pages written against the number of hours George spends per week on his dissertation. The scatter plot data points are plotted along with a best-fit line. The equation of the best-fit line is sought from the given options.

To identify the correct equation, let's first examine the slope and y-intercept of the line on the graph:

1. Slope (m): The slope is the rate at which the number of pages increases per hour. From the graph, the line rises by approximately 2 units for every 1 unit it runs horizontally, indicating that the slope $m = 2$.

2. Y-intercept (b): The y-intercept is the value where the line crosses the y-axis (when the number of hours $x = 0$). It appears to cross the y-axis at approximately 4, meaning $b = 4$.

So, the equation of the line appears to be:

$y = 2x + 4$

Looking at the provided options:

• A: $y = \frac{1}{2}x - 4$
• B: $y = 2x - 4$
• C: $y = 2x + 4$
• D: $y = 4x - 2$

The correct equation is:

C: $y = 2x + 4$

Would you like more details or have any questions about this solution?

Here are 5 questions related to this problem:

1. How would the graph look if the slope were negative?
2. What would the line represent if the y-intercept were zero?
3. How can we determine the slope of a line if we are given two data points?
4. What is the importance of the y-intercept in a real-world context?
5. How would the equation change if George's productivity decreased over time?

Tip: Understanding the relationship between the slope and the y-intercept in linear equations is crucial for interpreting graphs in real-world scenarios.