Question

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: 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 280 at increments of 40. A straight line joins the ordered pairs 0, 200 and 1, 160 and 2, 120 and 3, 80 and 4, 40 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)

Answer 1

Each week the amount of songs that need to download decreases by 40. So The rate of change is -40 songs each week. The initial value is 200 because that is the number of songs left to download.

Part B:

y = -40x + 200

Answer 2

PART A)

The rate of change is -40 songs each week, because the amount of songs left to be downloaded decrease by 40 every week.

the initial value is 200 at 0 weeks, which means that there are 200 songs to be downloaded at the beginning

PART B)

calculate the slope:
m = (y2- y1)/(x2 - x1) = (160 - 200)/(1 - 0)
m = -40
now use the line equation in form of point-slope
y - y1 = m(x - x1)
y - 200 = -40(x - 0)
y = -40x + 200