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)
(MAKE IT SOUND LIKE A FIFTH GRADER AND ALSO MAKE IT LESS THAN 200 WORDS ALSO JUDGING BY HOW ITS WRITTEN TRY TO MAKE IT SOUND LIKE THE LESSON)
Part A: The rate of change in this scenario is 20, because for every week that passes, Gina downloads 20 songs. The initial value is 100, which represents the starting point when Gina purchased the songs. When the graph starts at 100, it means that Gina has 100 songs left to download at the beginning.
To find the rate of change, we can use the formula: (y2 - y1) / (x2 - x1). Using the points (0, 100) and (1, 80), we get (80 - 100) / (1 - 0) = -20 / 1 = -20, but since we want a positive rate of change, we take the absolute value, 20.
Part B: The equation in slope-intercept form for this relationship is y = -20x + 100. In this equation, y represents the number of songs left to download, x represents the number of weeks passed, -20 is the rate of change (the slope), and 100 is the initial value. So, this equation shows how many songs Gina has left to download each week.