Question

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:
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)

Answer 1

Answer:

A. initial value = 100 (total amount of songs to download)

rate of change = -20 songs/week

B. y = -20x + 100

Step-by-step explanation:

A. The initial value of the function represented by the graph is its y-intercept point, that is, the value at which the function intercepts y-axis. In this case, this value is 100 songs. It represents the number of songs left before start to download them.

The rate of change is computed at follows:

[f(x2) - f(x1)]/(x2 - x1)

where (x1, f(x1)) and (x2, f(x2)) are two points on the line. Using (0, 100) and (1, 80), we get:

rate of change (80 - 100)/(1 - 0) = -20

This means that each week there are 20 songs less than the previous week.

B. In general terms, the slope-intercept form is:

y = mx + b

where m is the slope (which coincides with the rate of change), and b is the y-intercept (or initial value). Replacing with the results of part A:

y = -20x + 100

Step-by-step explanation:

Answer 2

Answer:

y = -20x + 100

Step-by-step explanation:

As per your requirement For Part B, the solution is

The equation in slope-intercept form to model the relations is below:-

To reach 2 points on the graph the line passes through

lets use p1(0, 100), p2(1, 80)

now we will compute the slope:

= -20

and now use line equation in form point-slope:

y - y1 = m(x - x1)

y - 100 = -20(x - 0)

y = -20x + 100