2. gina has borrowed 100 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: 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)

Part (a):
The rate of change would simply be the slope of the line. In our scenario, they represent the decrease in the number of songs to be downloaded as the weeks pass.
First, we would need to choose any two points on the graph.
I will choose points (0,100) and (5,0)
slope of the line is calculated using the following rule:
slope of the line = (y2 - y1) / (x2 - x1)
slope of the line = (0-100) / (5-0) = -20
Note: The slope is negative as the number of songs to be downloaded decrease as weeks pass. She starts originally with 100 songs and decreases at a rate of 20 songs / week

The initial value is the value of the y at x = 0. In our scenario, the initial value represents the number of songs to be downloaded originally before any weeks pass which is the 100 songs Gina plans to download
initial value = 100

Part (b):
The general form of the equation is:
y = mx + c
where:
m is the slope of the line = -20
c is the y-intercept (value of y at x = 0) = 100
Therefore, the equation of the line is:
y = -20x + 100

Hope this helps :)

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