Question

Kyla wants to add songs to her phone to listen to while she is riding on the bus. She bought 100 songs on her account.She is planning to download an equal number of songs each week for the next 5 weeks. The number of songs left to download, y, for a certain number of weeks, c is shown in the graph.

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: Determine the rate of change and the initial value (2 points) of the function show on the graph. What does each represent in the scenario (2 points)? Show/Explain the work you completed to find the rate of change and initial value (2 points).

Part B: Using the information from Part A, write the equation that would model this relationship between x and y in slope-intercept form. (4 points)

Answer 1

Slope = - 20; intercept, c = 100

y = - 20x

Explanation:

The slope (s) = Rise / Run

using the pairs : (0, 100) and (5, 0)

x1 = 0 ; y1 = 100 ; x2 = 5 ; y2 = 0

Rise = (y2 - y1) = (0 - 100) = - 100

Run = (x2 - x1) = (5 - 0) = 5

Slope = - 100 / 5

Slope = - 20

Using the slope intercept relation :

y = mx + c

m = slope ; c = intercept

y = - 20x + c

Using the point (4, 20) to find c

20 = - 20(4) + c

20 = - 80 + c

20 + 80 = c

100 = c

Hence, c = 100

Slope, m = number of songs downloaded per week

c = Total number songs at week 0

The equation expressed in slope intercept form:

General form:

y = mx + c

m = - 20 ; c = 100

y = - 20x + 100