Question

Help me figure this out!
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Answer 1

I think it might be week 7.

Answer 2

see attached as to how to pick out the 2 points

Answer 3

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

Answer 4

okay...

Answer 5

tell me what you get for each equation

Answer 6

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

Answer 7

by using the slope formula

\[\Large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]

Answer 8

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)

Answer 9

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.

Answer 10

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

Answer 11

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.

Answer 12

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)

Answer 13

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)

Answer 14

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...

Answer 15

so slope is 255?

Answer 16

yep, correct

Answer 17

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

Answer 18

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

Answer 19

more like this

y = mx+b

740 = 255*1 + b

b = ???

Answer 20

oh I see okay

Answer 21

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

Answer 22

485

Answer 23

good

Answer 24

so the revenue equation is y = 255x + 485

Answer 25

you now need the expenses equation

Answer 26

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

Answer 27

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

Answer 28

-160 ?

Answer 29

yep

Answer 30

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

Answer 31

3,010 = -160*1 + b

b = 3,170

Answer 32

very good

Answer 33

revenue equation: y = 255x + 485

expenses equation: y = -160x + 3170

Answer 34

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

Answer 35

do you know a website I can graph these?

Answer 36

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

Answer 37

you can use desmos

https://www.desmos.com/calculator

Answer 38

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

Answer 39

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

Answer 40

I just search for graph in geogebra?

Answer 41

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

Answer 42

desmos

Answer 43

ok let's use desmos then

Answer 44

type in each equation in their own line

Answer 45

and click the wrench on the right side to adjust the window

I have

xmin = -40
xmax = 40

ymin = -3000
ymax = 5000

Answer 46

this is what my graph looks like

Answer 47

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

Answer 48

see the attached image

Answer 49

nvm I changed it I have your settings now.

Answer 50

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

Answer 51

you may have to click twice

Answer 52

yeah they are 6.47 and 2135

Answer 53

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

Answer 54

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

Answer 55

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

Answer 56

yeah I see that okay.

Answer 57

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

Answer 58

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

Answer 59

yeah it makes way more sense now :)