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)
Part A:
To find the rate of change, we need to determine the change in y divided by the change in x.
The change in y is -20 (from 100 to 80) and the change in x is 1 (from 0 to 1).
The rate of change is therefore -20/1 = -20.
The rate of change represents the amount by which y changes for every 1 unit change in x. In this scenario, it represents the number of songs Gina is downloading each week.
To find the initial value, we look at the y-intercept of the graph, which is the point where x = 0. In this case, the y-intercept is 100.
The initial value represents the starting point of the graph, or the number of songs Gina had to download before she started downloading any songs each week.
Therefore, the rate of change is -20 songs per week and the initial value is 100 songs.
Part B:
The equation in slope-intercept form is y = mx + b, where m is the slope (rate of change) and b is the y-intercept (initial value).
From Part A, we found that the rate of change (m) is -20 and the initial value (b) is 100.
Therefore, the equation is: y = -20x + 100.
The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes:
A graph titled Distance Vs. Time is shown. The x axis is labeled Time in minutes and shows numbers 0, 1, 2, 3, 4, 5. The y axis is labeled Distance from Ocean Surface in meters. A straight line joins the points C at ordered pair 0,60, B at ordered pair 1, 100, A at ordered pair 2, 140, and the ordered pair 3, 180.
Part A: What is the slope of the graph between points A and B? And between points A and C? explain your reasoning (4 points)
Part B: What is the initial value and what doesit represent? (6 points)