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.

Question

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.

iGreen · Answer

Wait, you want help on this or the one in your dms?

Jiren · Answer

This one

iGreen · Answer

Can you get a picture of this one?

Jiren · Answer

yea sure

Jiren · Answer

https://broward.flvs.net/webdav/assessment_images/educator_mjprealgebra_v16/mjprealgebra_test2_m5_g1_p.jpg

iGreen · Answer

Uh, that doesn't work

Jiren · Answer

whats the image format on here

iGreen · Answer

wot? You could upload it to Gyazo like you did in DMs

Jiren · Answer

https://gyazo.com/118208a17f8a9339bac3fb3ab67811af

iGreen · Answer

Okay, do you know what average rate of change is?

Jiren · Answer

No i'm terrible at pre alg

iGreen · Answer

Rate of Change is just the slope

iGreen · Answer

Slope is just Rise/Run

iGreen · Answer

Can you calculate the slope for this line?

iGreen · Answer

Start at (0, 0), and then go to the next point...how much do you rise and how much do you run?

iGreen · Answer

From (0, 0) to (16, 2) @Jiren

iGreen · Answer

(2, 16)*

Jiren · Answer

Sorry IGreen I posted the wrong graph

Jiren · Answer

https://gyazo.com/a8042a9723a13942c233d1fcf0704abb here is the correct graph lol sorry

iGreen · Answer

Ah, okay, let's just use the slope formula then.

$\sf m=\dfrac{y_2-y_1}{x_2-x_1}$

Choose any two points and plug them in.

Jiren · Answer

Thats its?

iGreen · Answer

We're calculating the rate of change, which is the slope. Choose any two points from the graph.

Jiren · Answer

2,30

iGreen · Answer

That's not a point on the graph, let's use (1, 120) and (2, 90).

iGreen · Answer

(x1, y1), (x2, y2)

Can you plug them into the slope formula?

Jiren · Answer

Yes I think

iGreen · Answer

Okay, tell me what you come up with.

iGreen · Answer

(1, 120), (2, 90)
(x1, y1), (x2, y2)

$\sf m=\dfrac{y_2-y_1}{x_2-x_1}$

Jiren · Answer

this is part a?*

iGreen · Answer

Yes

iGreen · Answer

Did you find the slope?

iGreen · Answer

$\sf m=\dfrac{90-120}{2-1}$

Simplify

iGreen · Answer

@Jiren Did you get anything?