Question

1.Change the equation into slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all of your work.
2.Describe how you would graph this line using the slope-intercept method. Be sure to write in complete sentences.
3.Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
4.Graph the function using one of the following two options below. One the graph, make sure to label the intercepts

Answer 1

I really need the answers soon to finish my homework. I am really confused by the explaining part in question 3

Answer 2

Do you have an equation they gave you?

Answer 3

let me check I think so

Answer 4

2x + 3y = 1,200

Answer 5

I already did the homework now(and somehow got a 100%) but I didn't understand what I was doing and wouldn't be able to do it on another question without help so I would like to know how to do it because it will be on my test.

Answer 6

I have another question after this too.

Answer 7

I am not sure about #3, but I could help on the rest

Answer 8

ok

Answer 9

Ok, so the equation is 2x + 3y = 1200. We need to make this look like y = mx + b

Answer 10

ok

Answer 11

Do you have any guesses on how to do that?

Answer 12

First we need to move +2x to the right side

Answer 13

Also,
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Answer 14

thanks

Answer 15

and I think you subtract -2x from each side

Answer 16

Yep

Answer 17

So once you subtract 2x, you get 3y = -2x + 1200

Answer 18

yes what's next? I know the final answer but I don't understand the work

Answer 19

Ok, now divide everything by 3 to isolate y

Answer 20

ok so I get y=2/3x+400?

Answer 21

Yes!

Answer 22

That is how you get the answer for the first one.

Answer 23

oh ok thx now I understand the work for that one

Answer 24

Ok, now for the second one, we have to explain how to graph it

Answer 25

There is a simple way and a hard way to graph, we will try the easy way first

Answer 26

ok

Answer 27

Now we have the equation \(\sf y~=~\dfrac{2}{3}x~+~400\). The simple way is to plug in any value for x, and come up with y. For example, if I plug in 1 for x:
\(\sf y~=~\dfrac{2}{3}(1)~+~400\\\)
\(\sf y~=~\dfrac{2}{3}~+~400\\\)
\(\sf 400.\overline{666}\)

Answer 28

We can tell from the slope that we have to go up 3 x values to get a whole number for y

Answer 29

um ok

Answer 30

Oh wait, do you know what the slope and y-intercept is?

Answer 31

yes

Answer 32

Ok, do you see how I am doing this?

Answer 33

Actually it would be y = -2/3x + 400

Answer 34

Not 2/3..

Because you originally had -2, and dividing 3, will give you -2/3..

Answer 35

Oh whoops, thanks for catching that @iGreen

Answer 36

y = -2/3x + 400 answers your question for #1

It's in Slope Intercept form..now you have to say what the slope and y-intercept are..do you know what the slope and y-intercept are for this equation? @horsegirl27

Answer 37

slope is -2/3and y-intercept is 400 I think

Answer 38

You got it!

So that answers #1 for you.

Answer 39

Yep! ^_^

Answer 40

oh thank you!

Answer 41

Now for #2, we can say to plot the y-intercept, which we know as 400, then we draw a line with a slope of -2/3 through it.

Answer 42

For #3, writing an equation in function notation is just replacing 'y' with 'f(x)'.

\(y = -\dfrac{2}{3} + 400\)

So what do you get?

Answer 43

ok and because rise over run the slope would be down 2 over 3 right? and it will go through 400 on the y-axis but what about on the x-axis?

Answer 44

Yep, I think @iGreen has this one :)

Answer 45

Drawing the line will tell you everything..you don't need the x-axis.

Answer 46

yes but thanks @sleepyjess for helping

Answer 47

oh ok

Answer 48

Yep! ^^

Answer 49

and I got f(x)=2x+400. Or is it f(x)=-2/3x+400?

Answer 50

Note: this is not the most accurate graph

Answer 51

All you do for function notation is replace y with f(x)

Answer 52

Everything else stays the same

Answer 53

so it's f(x)=-2/3x+400?

Answer 54

Yes

Answer 55

What are the 2 options for part 4?

Answer 56

oh ok so not f(x)=2x+400