Question

(05.03 MC)

Ivy has purchased 150 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 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.

Answer 1

Part A:

To find the rate of change:

m = (150 - 120) / (0 - 1) because the slope formula is:

m = (
`y_(2) - y_(1)`) / (
`x_(2) - x_(1)`)

m = (150 - 120) / (0 - 1) is equal to:

m = 30/-1
Or -30.

So the rate of change is -30.

The initial value is just 150, because as the x value is 0, the y value is 150.

The rate of change represents how she has to download 30 less songs onto her music player each week. The initial value means she originally had 150 songs she needed to download.

Part B:

Slope intercept form is y = mx + b.

In this case, we already can figure out everything because the y intercept is said, when it says a straight line joins the ordered pairs 0, 150, and 1, 120... etc.

So since the x value in that point was 0, we then know that that 150 must be the y intercept.

So since we know the slope, m, as well (-30) we can just fit everything into this equation.

y = -30x + 150