Let's analyze this step by step.

Analyzing the graph:

1. The initial value of a function is the $y$-intercept of the graph, i.e., the value of $y$ when $x = 0$. From the provided graph, it appears the $y$-intercept for Songs-Galore is not directly shown but can be calculated based on the trend of the line.

2. The rate of change (or slope) can be calculated using the formula: $\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$ For the Songs-Galore function, points (2, 15) and (8, 24) are given. We can calculate: $\text{slope for Songs-Galore} = \frac{24 - 15}{8 - 2} = \frac{9}{6} = 1.5$

3. To compare with Easy Tracks, the question mentions it separately. Without seeing Easy Tracks’ line directly on the graph, I assume its initial value and slope are given elsewhere in the exercise.

Filling in the blanks:

1. Initial Value:

   • The initial value for Songs-Galore (from the graph's trend) seems to align with the $y$-axis intercept.
   • Compare this to Easy Tracks (value provided or inferred).

2. Greater Initial Value:

   • Compare the initial values of Easy Tracks and Songs-Galore.

3. Rate of Change:

   • Songs-Galore has a slope of $1.5$.
   • Determine Easy Tracks’ rate of change to complete the comparison.

Would you like me to deduce missing details or guide you further on solving these types of problems? Here are some related questions you can explore:

Questions:

1. How do you find the slope from two given points on a line?
2. What does the $y$-intercept represent in real-life situations like this graph?
3. How can you graphically compare two functions’ rates of change?
4. If given only two points, how can you write the equation of the line?
5. How can you determine the better value (price/song) between the two companies?

Tip: Always check units carefully when comparing rates of change to understand what they represent in real-world terms.