Question

how do i find the points to graph these two linear sentences x+2y<=12 and 3x-y>=6? Please show all work.

Answer 1

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

Answer 2

you graph the boundary lines:

x+2y = 12 and 3x-y = 6

Answer 3

pick a point not on the line; (0,0) is an easy testing point

Answer 4

and if those make the equation true; then the side with that point is good, shade it; if false, go with the other side

Answer 5

ah so you can start with any natural number then and plug it into the formula? or no?

Answer 6

equation*

Answer 7

you can, but it helps to see that these are line equations; and you just need 2 points to draw a line with right?

Answer 8

the lines themselves are boundaries for the inequalities; so graph them first;

Answer 9

x+2y = 12 and 3x-y = 6; graph these lines so you establish the boundaries for the inequalitites

Answer 10

then pick a point that is NOT on the line to test for a result. that point will be on one side or the other of the line right? The most conviennt point to test is the origin: (0,0)

x+2y<=12 and 3x-y>=6

0+2(0)<=12 and 3(0)-(0)>=6

0 <= 12 and 0 >=6
true false

Answer 11

all the points that make a true stament get shaded; all th epoints that make it false... shade the other side of the line

Answer 12

okay i get it use typing it out really help me... :D

Answer 13

lol you* typing it out...

Answer 14

school comp is slow lol

Answer 15

its so weird maybe im asking the wrong question because my book is giving me 2 lines not one for the answer

Answer 16

the answer has 2 lines; I just demonstrated with 1

Answer 17

o sorry i get it now. i was confused for a second so then i can use the same points (0,0) for the second variable correct?

Answer 18

more like this

yes, as long as (0,0)aint on the line your testing, its the easiest one to use

Answer 19

it is the common area that the two have that are solutions

Answer 20

gd i still am confused so now that we have that one line how do we plot the other line? because in the above answer you plug (0,0) into both variables

Answer 21

lemme just write this out and see if i can figure it out before i frustrate you.

Answer 22

you really make 2 solution sets and where they overlap, is the area I shaded

Answer 23

how do i give you a good review?

Answer 24

you might have to hit f5 to refresh your browser and youll see a 'good answer' button next to my name

Answer 25

know a good free graphing programing?

Answer 26

program*

Answer 27

hmmm.... i use wolframalpha.com alot ; but it suits me

Answer 28

http://www.wolframalpha.com/input/?i=3x-y%3E%3D6+and++x%2B2y%3C%3D12

Answer 29

tyvm

Answer 30

youre welcome :)