(05.03 MC) Gina has purchased 100 songs from the internet. 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:

A graph titled Song Downloading shows Number of Weeks on x-axis and Number of Songs Left to Download on y-axis. The x-axis scale is shown from 0 to 5 at increments of 1, and the y-axis scale is shown from 0 to 140 at increments of 20. A straight line joins the ordered pairs 0, 100 and 1, 80 and 2, 60 and 3, 40 and 4, 20 and 5, 0.
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. initial value = 100 (total amount of songs to download)

rate of change = -20 songs/week

B. y = -20x + 100

Step-by-step explanation:

A. The initial value of the function represented by the graph is its y-intercept point, that is, the value at which the function intercepts y-axis. In this case, this value is 100 songs. It represents the number of songs left before start to download them.

The rate of change is computed at follows:

[f(x2) - f(x1)]/(x2 - x1)

where (x1, f(x1)) and (x2, f(x2)) are two points on the line. Using (0, 100) and (1, 80), we get:

rate of change (80 - 100)/(1 - 0) = -20

This means that each week there are 20 songs less than the previous week.

B. In general terms, the slope-intercept form is:

y = mx + b

where m is the slope (which coincides with the rate of change), and b is the y-intercept (or initial value). Replacing with the results of part A:

y = -20x + 100

step-by-step explanation:

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step-by-step explanation: