Let's break down the problem provided.

We are given:

• For 3 hours of work, Sofia earns $30.60.
• For 5 hours of work, she earns $51.
• For 6 hours of work, she earns $61.20.

Part (a) - Graph:

You need to plot the points on the graph where:

• The x-axis represents hours worked.
• The y-axis represents earnings.

You should plot the following points based on the given information:

• (3, 30.60)
• (5, 51)
• (6, 61.20)

After plotting these points, draw a line through them to represent the relationship between hours worked and earnings.

Part (b) - Slope:

The slope of the line represents the rate of change between hours worked and earnings. To calculate the slope $m$, use the formula:

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

Let's use two points: (3, 30.60) and (5, 51). $m = \frac{51 - 30.60}{5 - 3} = \frac{20.40}{2} = 10.20$

The slope is $10.20$.

Part (c) - Meaning of the Slope:

The slope of the line represents Sofia's earnings per hour. Since the slope is 10.20, this means that for every hour Sofia works, she earns $10.20.

This slope also relates to the unit rate of earnings. The unit rate (how much she earns per hour) is exactly the slope, meaning Sofia earns $10.20 for each hour worked.

Do you want further details on any of these points or have any questions?

Here are some additional related questions:

1. How do we find the y-intercept of the line?
2. Can you calculate the total earnings for 8 hours of work using the slope?
3. How would the graph change if Sofia’s hourly rate increased?
4. What does it mean if the slope of a line is 0 in this context?
5. Can the relationship between hours worked and earnings ever be non-linear?

Tip: The slope represents the rate of change in many real-life situations, especially in linear relationships like time vs. earnings.