Question

A company produces accessories for smart phones and tablets. The profit on each smart phone case is $2 and the profit on each tablet case is $3. The company made a profit of $1,200 on the cases last month. The equation 2x + 3y = 1,200 represents the company's profit from cases last month, where x is the number of smart phone cases sold and y is the number of tablet cases sold.
2. Describe how you would graph this line using the slope-intercept method.
Be sure to write in complete sentences.

Answer 1

Do you know what slope-intercept form is?

Answer 2

the slope-intercept form is y=mx+b where m is the gradient/slope and b is the y-intercept.

Answer 3

Right. So the first step is to get the equation we have looking like that.

Answer 4

ok but how do I do that

Answer 5

Solve \(2x + 3y = 1200\) for y.

Answer 6

400

Answer 7

Er.. it has to be in the form of an equation. y = something.

Answer 8

oh y=400

Answer 9

What'd you do with x?

Answer 10

I multiplied it by 0

Answer 11

Ok, well, unless you want to solve for where x = 0, you shouldn't do that.
\[3y = 1200 - 2x\]\[y = 400 - \frac{2}{3}x\]

Answer 12

ooooo so would that be answer or is there more steps

Answer 13

That's the equation in y=mx+b form. Now you know the slope and y intercept so you can graph it. The actual answer is to explain what we did, so... you'll have to do that. But it's basically the answer.

Answer 14

okay thank you since you helped me with that can you tell me how to turn them into function notations

Answer 15

What do you mean? You mean like f(x)?

Answer 16

I don't know all it says is
3.Write the equation in function notation.
Explain what the graph of the function represents.
Be sure to use complete sentences.

Answer 17

Yeah. That's f(x). You just write the equation in terms of f(x).

Answer 18

how do I do that

Answer 19

Once you've solved for y (that is, it's in a form like \(y = mx + b\)) you just replace y with f(x).

Answer 20

so fx= 400-2/3x then what because im supposed to graph the equation after I put it in a notation

Answer 21

Ok. Well, you know the slope and the y-intercept. So you can graph it from that.

Answer 22

wait whats the slope again

Answer 23

\[y = mx + b\]m is the slope

Answer 24

oh I thought m was the y intercept

Answer 25

o wait nvm I got confused

Answer 26

No, b is the y-intercept.
(For some reason.)

Answer 27

so since 2/3 is the slope how do I write that as a function

Answer 28

do I do 2/3(400)

Answer 29

I'm confused as to what you're asking.

Answer 30

well because it wants me to write it as a notation then graph it so would the answer be 2/3(400). really I just need to know the notation so I can graph it

Answer 31

The notation is \(f(x) = mx + b\)
Where m is the slope and b is the y-intercept

Answer 32

oooo okay I understand

Answer 33

Good!

Answer 34

just one last question and then im all done, the question is also apart of the function notation question. what does the graph of the function represent?

Answer 35

I'm actually not sure what they're asking there. Profit of smart phone cases vs profit of tablet cases, I guess.

Answer 36

Wait so the slope is 400 and the y intercept is 2/3?
I'm confused here.