Question

[6.06] The graph below is represented by which system of inequalities?

Two lines intersecting on a coordinate plane. The first line is a solid line that passes through (-3, 2) and (0, 3) and is shaded below the line. The second line is a dashed line that passes through the points (-1, 3) and (0, 1) and is shaded above the line.

-x + 3y < 9
y > -2x + 1

-x + 3y less than or greater to 9
y > -2x + 1

-x + 3y < 9
y greater than or equal to -2x + 1

None of these systems represent the graph shown.

Answer 1

you have a solid line, so one of the inequalities will have either a \(\Large \le\) or a \(\Large \ge\)

Answer 2

so that definitely rules out choice A

Answer 3

Ok, thx, the only equations with the line underneath is b or c. :)

Answer 4

yes, the answer could be D too, since we haven't determined whether it's B or C yet

Answer 5

Yes:) I don't understand how to do inequalities, does the colors have to do with anything?

Answer 6

the colors just correspond to the individual shaded regions

Answer 7

the green area is the overlapping region of the two inequalities

Answer 8

Oh, okay, lol! :D

Answer 9

overlapping of yellow and blue regions

Answer 10

look at the solid line, then look at the yellow region, it's below the solid line, agreed?

Answer 11

Hmm, which equation goes with the dotted area of the graph, and which with the solid line?

Answer 12

Yeah, you r right! :D

Answer 13

so this means that the inequality symbol that that represents that shaded region must be a \(\Large \le\)

Answer 14

in choice B, you said "less than or greater to ", which one is it?

Answer 15

yeah.In choice B, it said...

Answer 16

It was the greater THAN SYMBOL, WITH A SOLID LINE. :)

Answer 17

so it's a \(\Large \ge\) sign for choice B

Answer 18

Nope, sorry, I meant the other one.

Answer 19

less than. :)

Answer 20

ok, so it's a \(\Large \le\) sign for choice B

Answer 21

but the solid line is right. :)

Answer 22

anyways, because the solid line has a the shaded region below the solid line, this means that we're dealing with a \(\Large \le\) sign

Answer 23

Actually none of the answer choiices have that symbol, so it would probs be d?

Answer 24

doesn't choice B have that symbol?

Answer 25

post a screenshot of the answer choices

Answer 26

Ho do you do that?

Answer 27

hit printscreen (key on your keyboard, above the insert key)

paste the image into paint

save

then attach to show me

Answer 28

the printscreen key used to print the screen (back in the old days), but now it's used to copy an image of exactly what you see on the screen (so you can effectively share your screen so to speak)

Answer 29

yEAH, I WISH I COULD DO THAT, BUT MY COMPUTER DOESN'T HAVE WINDOWS PAINT, UNFORTUNATELY. :)

Answer 30

no ms paint? weird

Answer 31

what happens when you type

windows key + R

then type in "mspaint" without quotes and hit enter

Answer 32

Yeah, because we have Windows 8, but it has nothing. :)

Answer 33

oh, hmm one sec

Answer 34

see this page

http://www.eightforums.com/tutorials/2596-screenshot-create-paint-windows-8-a.html

Answer 35

Thx, I can only describe the choices, do you have Windows 8?

Answer 36

no, i have xp

Answer 37

btw, you should have paint (or some basic drawing/painting image program)...seems really odd how windows 8 (which is supposed to be an upgrade) doesn't have that

Answer 38

yeah, it is really dumb, there is nothing on this computer, I like Windows 7 better, but I am trying to take the screenshot. :) what is the windows key?

Answer 39

it's a key that looks like this

http://cdn-static.zdnet.com/i/story/61/45/009361/20070529-windowskey-f1.jpg

Answer 40

it's near the bottom of the keyboard (lower left near the "control" and "alt" keys)

Answer 41

Ok, I got it! Finally! here it is. :)

Answer 42

ok thanks

Answer 43

You r welcome, took me a while though. :)

Answer 44

choice B does have a \(\Large \le\) sign

Answer 45

just as I thought

Answer 46

that's ok, you'll get quicker at it with enough practice

Answer 47

oh, okay. :)

Answer 48

so choice C is eliminated

Answer 49

because the shaded region is below the solid line (not above)

Answer 50

so the answer is either B or D

Answer 51

Hmm...ok, so now b or d?

Answer 52

notice how the blue region is above the dashed line, and choice B has a > sign

so that adds more evidence that choice B is the answer (it doesn't fully conclude it is though)

to fully verify that choice B is the answer (or not), we need to see if the points correspond to the equations

Answer 53

look at the solid line

the points (0,3) and (3,4) are on the solid line

Answer 54

Yes, I see it! :D

Answer 55

so you need to see if both (0,3) and (3,4) satisfy the equation

-x+3y = 9

Answer 56

I plugged in both and they both do equal 9. :)

Answer 57

good, so (0,3) and (3,4) lie on this solid line, this confirms that at least one of the equations is indeed \(\Large -x+3y \le 9\)

Answer 58

now identify 2 points that lie on the dashed line

then plug in them into y > -2x+1

Answer 59

i mean y = -2x+1

Answer 60

(1,-1) (2,-3)?

Answer 61

ok great

Answer 62

check to see if they work in y = -2x+1

Answer 63

I plugged x into the equation, and they both equal y. :)

Answer 64

good

Answer 65

so this is the last piece of verification, and you're done verifying that the answer is B

Answer 66

Ok, thx so much, can you help me with one more that I post up?

Answer 67

It is another post I'm going to do. :)

Answer 68

sure i can help

Answer 69

Ok, thx, I will post it up in a little while, so you can check then. :) thx for your help! It was so nice!

Answer 70

yw