Question

PLZ HELP 3 pionts

(05.03 MC) Ivy has borrowed 150 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 210 at increments of 30. A straight line joins the ordered pairs 0, 150 and 1, 120 and 2, 90 and 3, 60 and 4, 30 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

See below.

Explanation:

A) The rate of change would be dividing the number of songs wanted (150) by the number of weeks downloading (5).

150/5 = 30

As the total quantity wanted is becoming less every week the rate of change would be negative so it becomes -30.

The initial value is 150, which is the total number of songs she wants.

B)

We’ll use A(0, 150), and B(1, 120)

calculate the slope:

m = (y2- y1)/(x2 - x1) = (120 - 150)/(1 - 0)

(in other words: delta y / delta x)

m = -30

Finally, use the line equation in form point-slope:

y - y1 = m(x - x1)

y - 150 = -30(x - 0)

y = -30x + 150