OpenStudy (anonymous):

Help me figure this out! /

2 years ago
OpenStudy (anonymous):

I think it might be week 7.

2 years ago
OpenStudy (jim_thompson5910):

see attached as to how to pick out the 2 points

2 years ago
OpenStudy (jim_thompson5910):

hopefully you see how I get (1,740) and (2,995) use those two points to find the slope, then determine the y-intercept to figure out the entire equation of the line for the revenue repeat the same steps for the expenses to get that equation as well

2 years ago
OpenStudy (anonymous):

okay...

2 years ago
OpenStudy (jim_thompson5910):

tell me what you get for each equation

2 years ago
OpenStudy (anonymous):

wait how do I find the slope of those two points?

2 years ago
OpenStudy (jim_thompson5910):

by using the slope formula \[\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]

2 years ago
OpenStudy (jim_thompson5910):

essentially you subtract the y coordinates then subtract the x coordinates (same order as the y coordinates) and then divide the differences (y over x)

2 years ago
OpenStudy (anonymous):

um okay I didn't do that right. Which ones are y2 and y1 and x2 and x1? That's what I'm confused about.

2 years ago
OpenStudy (anonymous):

sorry I'm not getting this I'm really trying.

2 years ago
OpenStudy (jim_thompson5910):

let's say we had the two points (3,5) and (7,9) the first point is (3,5) so x1 = 3 and y1 = 5 the second point is (7,9) which means x2 = 7 and y2 = 9 plug these values into the slope formula \[\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\] \[\Large m = \frac{9-5}{7-3}\] \[\Large m = \frac{4}{4}\] \[\Large m = 1\] So the slope of this line is 1. This is not the answer to your question since it's a similar example; however, hopefully you can use these steps to find the slopes you need.

2 years ago
OpenStudy (anonymous):

yeah I understand that. What I don't know is what points I need to do. 1,740 and 2,995? I need 4 numbers to figure out the slope. (Like in your example 3,5 and 7,9)

2 years ago
OpenStudy (jim_thompson5910):

so in your case, the revenue one will have x1 = 1 y1 = 740 since the first point is (1,740) x2 = 2 y2 = 995 since the second point is (2,995)

2 years ago
OpenStudy (anonymous):

Yeah that's what I did at first I did the 1 and 2. I wasn't sure if that was correct. Shoulda just types it anyway. Okay...

2 years ago
OpenStudy (anonymous):

so slope is 255?

2 years ago
OpenStudy (jim_thompson5910):

yep, correct

2 years ago
OpenStudy (jim_thompson5910):

use a point, say (1,740) and the slope m = 255 to find the value of b use y = mx+b plug in the slope m = 255 and (x,y) = (1,740) and solve for b

2 years ago
OpenStudy (anonymous):

1,740 = 255 * 1,740 + b? what

2 years ago
OpenStudy (jim_thompson5910):

more like this y = mx+b 740 = 255*1 + b b = ???

2 years ago
OpenStudy (anonymous):

oh I see okay

2 years ago
OpenStudy (jim_thompson5910):

notice how for (1,740) x = 1 y = 740

2 years ago
OpenStudy (anonymous):

485

2 years ago
OpenStudy (jim_thompson5910):

good

2 years ago
OpenStudy (jim_thompson5910):

so the revenue equation is y = 255x + 485

2 years ago
OpenStudy (jim_thompson5910):

you now need the expenses equation

2 years ago
OpenStudy (anonymous):

aw man okay. Thanks for going through this w/ me. It's really appreciated.

2 years ago
OpenStudy (jim_thompson5910):

sure thing, tell me what you get for the slope of the expenses

2 years ago
OpenStudy (anonymous):

-160 ?

2 years ago
OpenStudy (jim_thompson5910):

yep

2 years ago
OpenStudy (jim_thompson5910):

now use one of the two points, and the slope, to find the value of b

2 years ago
OpenStudy (anonymous):

3,010 = -160*1 + b b = 3,170

2 years ago
OpenStudy (jim_thompson5910):

very good

2 years ago
OpenStudy (jim_thompson5910):

revenue equation: y = 255x + 485 expenses equation: y = -160x + 3170

2 years ago
OpenStudy (jim_thompson5910):

the intersection point of the two lines represents the point in time when revenue = expenses

2 years ago
OpenStudy (anonymous):

do you know a website I can graph these?

2 years ago
OpenStudy (jim_thompson5910):

or you can use substitution to solve the system y = 255x + 485 ... equation 1 -160x + 3170 = 255x + 485 ... plug in equation 2 solve for x

2 years ago
OpenStudy (jim_thompson5910):

or geogebra (that's what I'm using). It comes as a download or you can use the online (nondownloadable) version

2 years ago
OpenStudy (jim_thompson5910):

don't forget to change the window so you can see both lines

2 years ago
OpenStudy (anonymous):

I just search for graph in geogebra?

2 years ago
OpenStudy (jim_thompson5910):

which one are you more familiar with? geogebra or desmos?

2 years ago
OpenStudy (anonymous):

desmos

2 years ago
OpenStudy (jim_thompson5910):

ok let's use desmos then

2 years ago
OpenStudy (jim_thompson5910):

type in each equation in their own line

2 years ago
OpenStudy (jim_thompson5910):

and click the wrench on the right side to adjust the window I have xmin = -40 xmax = 40 ymin = -3000 ymax = 5000

2 years ago
OpenStudy (anonymous):

this is what my graph looks like

2 years ago
OpenStudy (anonymous):

idk what's wrong. the wrench doesn't allow me to adjust to those settings.

2 years ago
OpenStudy (jim_thompson5910):

see the attached image

2 years ago
OpenStudy (anonymous):

nvm I changed it I have your settings now.

2 years ago
OpenStudy (jim_thompson5910):

click the intersection point and you should see a popup text box with the coordinates of the intersection point

2 years ago
OpenStudy (jim_thompson5910):

you may have to click twice

2 years ago
OpenStudy (anonymous):

yeah they are 6.47 and 2135

2 years ago
OpenStudy (jim_thompson5910):

so when x = 6.47 roughly is when the revenue and expenses are the same it's between week 6 and week 7. I would say that it's during week 6 since week 7 is when revenue > expenses

2 years ago
OpenStudy (anonymous):

so since week 6 is closer that will be the best bet.

2 years ago
OpenStudy (jim_thompson5910):

well if x was say x = 6.99 I would still go for week 6 if I said "week 7" then that would imply everything from 7.00 to 7.99 but that's when the revenue is larger than expenses

2 years ago
OpenStudy (anonymous):

yeah I see that okay.

2 years ago
OpenStudy (anonymous):

I super appreciate you helping me with this. Like you are the GOAT I wish I could give you all the medals.

2 years ago
OpenStudy (jim_thompson5910):

lol I'm glad I could help out and that it's making more sense now

2 years ago
OpenStudy (anonymous):

yeah it makes way more sense now :)

2 years ago