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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.

Select the equation for the line of best fit shown in the graph, which depicts the relationship between the number of pages written and the number of hours George spends per week on his dissertation.

Learn how to determine the equation of the line of best fit from a scatter plot, featuring a real-world example of George's dissertation progress. This problem covers key concepts such as linear equations, slope-intercept form, and interpreting data from scatter plots, suitable for students in Grades 9-12.

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