Ivy has borrowed 150 songs from her friend. She plans to download an equal number of songs on her music player each week for 5 weeks. The graph shows the number of songs left to download, y, for a certain number of weeks, x:

Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario? Show your work to find the rate of change and initial value. (6 points)
Part B: Write an equation in slope-intercept form to model the relationship between x and y. (4 points)

A) The rate of change is -30, and it represents the number of songs taken off of her download list each week.
The initial value is 150, and it represents the number of songs she wants to download to begin with.

B) y = -30x + 150

Explanation
A) The rate of change can be found by using the slope formula between the first two points, (0, 150) and (1, 120):
m=(y₂-y₁)/(x₂-x₁) = (120-150)/(1-0) = -30/1 = -30

The initial value is the y-value of the first point on the graph, (0, 150).

B) The equation is in slope-intercept form, y=mx+b, where m represents the slope and b represents the y-intercept. The slope is the rate of change that we found in part A; the y-intercept is the initial value we found in part A. This gives us the equation y=-30x+150.