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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.

Respuesta :

The rate of change is equal to (y2-y1)/(x2-x1) where (x1,y1)=((0,150) and (x2,y2)=(5,0). Therefore the rate of change equals (0-150)/((5-0)=-30 songs/week. This is equal to the slope of the line that goes through these two points. The initial value is the y coordinate of the point when x=0 which is 150. The equation of the line is y=-30x+150, and this is the slope-intercept form (y=my+b) where m is the slope of the line and b is the y-intercept.

Answer:

[tex]y = -30x+150[/tex] is the equation in slope intercept form

Rate of change = -30

Intial valu =150

Step-by-step explanation:

Given that 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.

Initially there will be 150 songs left, next week 120 songs, and so on.

Thus there is a decrease of 30 songs every week.

Hence slope = -30

y intercept = 150 (initial songs left)

So equation of line would be

[tex]y = -30x+150[/tex]

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