Question

PLEASE HELP ME

Answer 1

@TheSmartOne @iambatman @iGreen @PRAETORIAN.10 @pooja195 @SolomonZelman @DanJS @jim_thompson5910 @Jigglypuff123

Answer 2

@sleepyjess

Answer 3

Does this have to do with inequalities?

Answer 4

I would say so..

Answer 5

It looks shaded. And the lines are solid...

Answer 6

Well this should help you:
http://www.uzinggo.com/writing-system-linear-inequalities-corresponds-graph/systems-linear-equations-inequalities/algebra-1

Answer 7

that should help u

Answer 8

I know how to get the equations, I just have no idea on which inequality signs to use.

Answer 9

my computer is not opening up the link

Answer 10

@theEric

Answer 11

Still need a hand?

Answer 12

yes please

Answer 13

Okay!

Can you find the equations of those lines? And don't worry about the shaded region yet. We need to know those lines, because they are the boundaries to the shaded region.

Answer 14

ok

Answer 15

Cool! Let me know when you have the equations, or if you need a hand after giving it a try.

Answer 16

sorry it took me a while my computer

Answer 17

ok one sec

Answer 18

y=-2x i dont know but i will try again if this isn't right

Answer 19

It's not right, you're right.
So, there's something that I always do when I have to figure out a line equation from the graph.
First, I look for where the line goes through points on the grid exactly. So, they are integer points. For the one that goes from top left to bottom right, I see \((-1,5),\ (0,-1),\ (1,-7)\). Do you agree with those points?

Answer 20

yes i agree with these points

Answer 21

Okay! So, we have some points on the line. Those are just easiest to identify and work with.

Now we can find the slope, because we know that slope is the change in the \(y\) divided by the change in the \(x\). We need two points to have a slope. The formula would be
\(m=\dfrac{y_2-y_1}{x_2-x_1}\)
Are you okay with that formula?

Answer 22

You could also just count lines on the graph.. But this is more like how a math class would ask you to do it.

Answer 23

ok

Answer 24

im ok with the formula. and thats how you do it?

Answer 25

That's how you find the slope of the line! So we have a few points for that line, so we can make sure that the slope is the same between all the points. If the slopes are the same, then we have a problem. I'll just check two.
First, \((-1,5)\ \text{and }(1,-7)\)
\(m=\dfrac{(-7)-(5)}{(1)-(-1)}=\dfrac{-12}{2}=-6\)
Next, \((0,-1)\text{ and }(1,-7)\)
\(m=\dfrac{(-7)-(-1)}{(1)-(0)}=\dfrac{-6}1=-6\)

So we have the \(\it slope\) of the line! And then, to have the whole thing in \(y=mx+b\) form (slope-intercept), we need the \(y\)-intercept. That's where \(x=0\). We have a point like that already, \((0,-1)\). So, when the \(x\) is \(0\), the \(y\) is \(-1\). So the \(y\)-intercept is \(-1\).

So now we have the slope and \(y\)-intercept, so we know that the line is described by
\(y=-6x-1\)
Is that okay with you? Because you'll be doing this same thing for the next line later!

Answer 26

oh ok

Answer 27

Does that look okay to you?

Answer 28

Like, do you understand it? If not, maybe I could clear something up. I know I'm not always clear :P

Answer 29

no i understand it but thats all we have to do?

Answer 30

Okay! Well, that's finding the line!
The line is solid, rather than being dashes or dots, so we'll assume that it's part of the region.
Now, would you say that the shaded region is above that line, or below it?

Answer 31

below?

Answer 32

I agree! So the line is
\(y=-6x-1\), but the region is then
\(y\le-6x-1\)
Less than, because it is the lesser \(y\) values that are in the shaded region. And equal to, because the line itself is part of the shaded region.

Answer 33

y >= 3x + 2 and y<= -6x
are those correct, those are the two inequalities

Answer 34

i think i got it ?

Answer 35

yeah those look good to me

Answer 36

I agree!

Answer 37

Congrats!

Answer 38

Any questions?

Answer 39

y<=-6x is the line through the origin, it's y intercept is zero

Answer 40

The other has a slope of 3, and crosses y-axis at 2

Answer 41

Oh, right!
It was \(y\le-6x-1\)!

Answer 42

THe shaded area is the solution set that satisfies both inequalities

Answer 43

That's the one we just did.

Answer 44

Thanks @DanJS !

Answer 45

no , not -1, it goes through the origin

Answer 46

or maybe it is -1, yeah it looks like -1

Answer 47

you are right

Answer 48

Graph is kinda small

Answer 49

thanks both of you !

Answer 50

You're welcome!

@DanJS Yeah, it's blurry! I'm only confident that the \(y\)-intercept is \(-1\) because it lines up with the other points that I think are on the line :)