Question

Gina has borrowed 100 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:

http://prntscr.com/7183kw

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.

Help! D:

Answer 1

I know how slopes and initial values and everything work but for some reason I'm really stuck on this. :/

Answer 2

qhat grade math is this

Answer 3

the initial function is where the line cross the y axis...so its basically the y intercept.

the rate of change (slope) can be found by using two sets of points on the line and subbing them into the slope formula : slope(m) = (y2 - y1) / (x2 - x1)

Answer 4

@sstylesprettygirl 8th :)

Answer 5

@texaschic101 So the initial value is 100? And for the rate of change I'm still really stuck cause I don't know where to start I must sound so dumb haha

Answer 6

no..you do not sound dumb....and yes, the initial value is 100.

now we find the slope...I will pick 2 sets of points on the line
(0,100) and (1,80)

slope(m) = (y2 - y1) / (x2 - x1)
(0,100)...x1 = 0 and y1 = 100
(1,80)...x2 = 1 and y2 = 80
now we sub
slope(m) = (80 - 100) / (1 - 0)
slope(m) = -20

so your rate of change (slope) = -20
any questions ?

Answer 7

so your rate of change is -20....so basically that is saying that for every week, she downloads 20 songs.

your initial function is 100.... so basically this is saying that your function starts at 100 songs to download.

now we need it in slope-intercept form : y = mx + b
we know that our slope(m) = -20
now we can use either of our sets of points...(0,100)
now we need to sub
100 = -20(0) + b
100 = b

so your equation is : y = -20x + 100

Answer 8

if you have any questions, please ask :)

Answer 9

@texaschic101 may you help me, when you are able too please?

Answer 10

if you have to show your work on how to find the initial function....you can just use your equation y = -20x + 100.....and sub in 0 for x....and find y (your initial function

Answer 11

@texaschic101 Aaa! Thank you so much! Thanks for breaking it down too instead of just giving the answer because I have similar essay questions to this one so I really get how it works. If I need you again for another question are you okay with me asking for help again?

Answer 12

of course...thats what I am here for :)

Answer 13

@texaschic101 I think I have part B of this down but would you mind checking too and walking through part A with me? Here's the question:

The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes:

http://prntscr.com/718eeq

Part A: Describe how you can use similar triangles to explain why the slope of the graph between points A and B is the same as the slope of the graph between points A and C. (4 points)
Part B: What are the initial value and slope of the graph and what do they represent?

Answer 14

@texaschic101 For Part A I think it's because between A B and C they all have the same rise/run meaning they'd all be similar triangles. It'd be 2 over 1 for their rise over run and you can use triangles to find it? I'll find a better way to word it.

And for Part B I have the initial value at 60 but I'm still working on the slope.

Answer 15

@texaschic101 Okay this is what I have so far. Still really stuck on the slope.

Part A: The slope is the same throughout all the marked points on the graph. Imagine or fill in the rise/run between each point. When that's finished, you'd see that the triangles would look similar, the A and C just being a larger triangle which would explain/prove the same slope between points A and B/A and C. (The slope between A and B is 2 over 1 which is equal to 2. The slope between A and C is 4 over 2 which simplifies to 2).

Part B: The initial value is 60.

Yes or no so far? :D

Answer 16

@texaschic101 I hate to keep bothering but I think I'm finished. I dunno if this is 100% right though. What do you think? For part B.

Part B: The initial value is 60 and it represents the distance from the ocean surface. The slope is 40 because by taking the points on the graph (1, 100), (0, 60) and subtracting, you get 40. This represents the distance.