Eva has borrowed 200 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.
Part B: Write an equation in slope-intercept form to model the relationship between x and y. 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)
the initial value of the function is 200 at 0 weeks, that means that there are still 200 songs to be downloaded at the beginning.
The rate of change is -40 songs each week, that is because the amount of songs left to be downloaded decrease by 40 each week.
art B: Write an equation in slope-intercept form to model the relationship between x and y. (4 points)
lets use 2 points of the graph p1(0, 200), p2(1, 160)
calculate the slope:
m = (y2- y1)/(x2 - x1) = (160 - 200)/(1 - 0)
m = -40
and now use line equation in form point-slope:
y - y1 = m(x - x1)
y - 200 = -40(x - 0)
y = -40x + 200

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