Help please

- anonymous

Help please

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- anonymous

Choose the linear inequality that describes each graph.

##### 1 Attachment

- anonymous

y < – 4x – 2
y > – 4x – 2
y ≤ – 4x – 2
y < 4x – 2

- Zale101

Are you familiar with graphing inequalities?

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- anonymous

No, not really.. I barely understand Algebra

- Zale101

Can you graph a standard line?

- anonymous

Not really

- Zale101

What math level are you currently on?

- anonymous

Algebra 1B

- Zale101

Before learning to graph inequalities, you are taught to graph lines and plot basic points. Correct?

- anonymous

I really don't know.. because I took half of Algebra like independent studies there was no teacher to explain what I was taking.

- Zale101

Btw, asalaam walikum and i hope Yemen will be freed soon.

- Zale101

Okay. So then i'd have to tutor you on graphing lines. Are you ready?

- anonymous

wa alaikum asalam, and in shaa Allah hopefully thanks

- anonymous

Yes :)

- Zale101

Let's began with the first multiple choice.
y < – 4x – 2

- Zale101

Every line has an equation written similar to the slope intercept form. The slope intercept form of equation is written like this : \(\Large y=mx+b\)
m stands for slopes
b stands for y-intercept (where the line touches the y-axis and has a x=0)
and x and y are changing, while m and b are constants.

- Zale101

When we have inequalities, we'll have to try to see if from a y=mx+b perspective so we can get a sense on what line we are dealing with. To do that, you basically change any inequality symbols (>, <) to an equal sign.
So, \(\large y ~<~ – 4x – 2\)
Will eventually become, \(\Large y=-4x-2\)

- Zale101

The line is y=-4x-2
Is this equation already in a slope intercept form?

- anonymous

what does it mean when you have ≤ this sign

- Zale101

If we have this, let's say \(y\le x\)
That means all the y values are less than or equal to x are shaded and the line is straight and bold, not dashed. It would have been a dashed line if the symbols were just less than or greater than (<,>). But when we add an equal sign next to the inequality, than it becomes a bold line.
So, when graphing it, it will become like this.|dw:1439489341719:dw||dw:1439489445470:dw|

- Zale101

As you can see from the graph i drew, all the y-values on the bottom of the line is shaded because the inequality is y is less than or equal to x.

- Zale101

And the line is bold, not dashed, because there's an equal sign with the inequality.

- Zale101

Now, back to graphing the first multple choice y = – 4x – 2
Can you graph this?

- anonymous

okay I'll try to

- Zale101

Thanks. I like when students participate on their problems. It gives me the sense that they are trying their best on their work.

- Zale101

You can try. Allah M3ek :)

- anonymous

am I right so far |dw:1439489802302:dw|

- Zale101

Yes, you drew the Cartesian graph correctly. Now, you can go ahead and draw the line. It's okay if you make any mistakes because you have me to correct it for you.

- Zale101

Everyone makes mistakes, including me :)

- Zale101

You can start by quickly plotting two points, and draw a line across those two points.

- anonymous

okay so can u help me now, im not sure what im supposed to do

- Zale101

That's the easiest way to do it. There's also other ways to draw a line.

- Zale101

Okay @proud_yemeniah_ are you familiar with plotting points?

- anonymous

No

- Zale101

I will plot one point, and you do the second point. Make sure you follow along.
|dw:1439490142436:dw|

- Zale101

My first point is (0,-2)
You can pick whatever you want for x, i chose 0 and got -2 for y, and you can choose 1 if you want.

- Zale101

Makes sense?

- anonymous

so u just choose any number

- Zale101

Plotting points is all about choosing whatever number you want for x, and plug that number for x into the equation to get for y. Just like how I chose 0 and plugged that into y=-4(0)-2 and got -2 for y.
Yes, you can choose any number.

- Zale101

What number would you like to choose?

- anonymous

so can I choose for example 3 or 2

- Zale101

Yes, whatever you want. What number will you choose?

- anonymous

I'll choose 2

- Zale101

plug that into the equation and tell me what you got for y

- Zale101

and i'll have to brb

- anonymous

okay, -4 (2) -2 ?

- anonymous

You can help me when u come back

- Zale101

I'm back.
So you did:
y=-4(2)-2
y=-8-2
y= ? what is y?

- anonymous

-10?

- Zale101

Yes. So we have two points.
(0,2) and (2, -10)
Can you plot these two points on this graph i drew?
|dw:1439491250235:dw|

- Zale101

this is for the line y=-4x-2

- anonymous

I don't know how am I supposed to do it

- Zale101

Can you plot (2,-10)?

- Zale101

SOrry, i did something wrong

- anonymous

its okay, so -10 is Y?

- Zale101

|dw:1439491783291:dw|

- Zale101

yes, -10 is a y-value

- Zale101

(x,y)
On a point, x is first, then y comes second.

- Zale101

Now, before you draw a line. Is the line dashed or bold in this inequality y < – 4x – 2 ?

- Zale101

Carefully look at the inequality symbol.

- anonymous

dashed?

- Zale101

Yes. So, our two points that we plotted we \((0,-2)\) and \((2,-10)\)
We plotted those. The line is dashed. |dw:1439492035470:dw|

- Zale101

What part of the graph is shaded, right or left?

- anonymous

umm right

- Zale101

y < – 4x – 2
y is less than -4x-2

- Zale101

I'll change the wording. Is the graph shaded on the top or bottom of the graph?

- anonymous

the bottom?

- Zale101

Yes! :)|dw:1439492292123:dw|

- Zale101

Does this look like the graph that was shown to you?

- anonymous

No, this is the graph that was shown to me

##### 1 Attachment

- anonymous

the right side was shaded

- Zale101

Nope. It doesn't doe A is incorrect. We know from the graph that the line is dashed, that means the inequality is show as < or >
We also know that the line is positive because it continuously goes up to the right on the positive direction.
The first choice y < – 4x – 2 went downwards because it was negative 4x-2.
We also know that the graph is less than than or < because the graph is shaded on the bottom of the line.

- Zale101

From all those choices, which choice best fits the description.?

- anonymous

well if negative doesn't work then it may be D

- Zale101

Yes.

- Zale101

I'm sorry if i have given you a hard time.

- Zale101

Now that you know how to graph a line and inequalities, then i have done my mission :)

- anonymous

Oh thank you very much.. No I actually liked going thru it and solving it together

- Zale101

Anytime. Good luck and take care!

- anonymous

You too thanks :) @Zale101

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