Help me figure this out! /
I think it might be week 7.
see attached as to how to pick out the 2 points
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
okay...
tell me what you get for each equation
wait how do I find the slope of those two points?
by using the slope formula \[\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]
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)
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.
sorry I'm not getting this I'm really trying.
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.
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)
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)
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...
so slope is 255?
yep, correct
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
1,740 = 255 * 1,740 + b? what
more like this y = mx+b 740 = 255*1 + b b = ???
oh I see okay
notice how for (1,740) x = 1 y = 740
485
good
so the revenue equation is y = 255x + 485
you now need the expenses equation
aw man okay. Thanks for going through this w/ me. It's really appreciated.
sure thing, tell me what you get for the slope of the expenses
-160 ?
yep
now use one of the two points, and the slope, to find the value of b
3,010 = -160*1 + b b = 3,170
very good
revenue equation: y = 255x + 485 expenses equation: y = -160x + 3170
the intersection point of the two lines represents the point in time when revenue = expenses
do you know a website I can graph these?
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
or geogebra (that's what I'm using). It comes as a download or you can use the online (nondownloadable) version
don't forget to change the window so you can see both lines
I just search for graph in geogebra?
which one are you more familiar with? geogebra or desmos?
desmos
ok let's use desmos then
type in each equation in their own line
and click the wrench on the right side to adjust the window I have xmin = -40 xmax = 40 ymin = -3000 ymax = 5000
this is what my graph looks like
idk what's wrong. the wrench doesn't allow me to adjust to those settings.
see the attached image
nvm I changed it I have your settings now.
click the intersection point and you should see a popup text box with the coordinates of the intersection point
you may have to click twice
yeah they are 6.47 and 2135
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
so since week 6 is closer that will be the best bet.
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
yeah I see that okay.
I super appreciate you helping me with this. Like you are the GOAT I wish I could give you all the medals.
lol I'm glad I could help out and that it's making more sense now
yeah it makes way more sense now :)
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