Part A: Using the graph above, create a system of inequalities that only contain points A and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points)
Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A. (3 points)
Part C: William can only attend a school in his designated zone. William's zone is defined by y < -x - 1. Explain how you can identify the schools that William is allowed to attend. (2 points)

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- MeowLover17

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- MeowLover17

- MeowLover17

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- MeowLover17

- MeowLover17

Hey Z4 Got any input??

- MeowLover17

- MeowLover17

Hmm

- Z4K4R1Y4

|dw:1433034312051:dw|

- MeowLover17

So what do i answer for part A?

- MeowLover17

Like where is the system of inequalities or how do i make it???

- MeowLover17

Jim please help

- jim_thompson5910

you can make up anything you want BUT it has to be where the solution for both has to have A and E in it (and only those two points)

- jim_thompson5910

|dw:1433034502120:dw|

- jim_thompson5910

|dw:1433034513862:dw|

- jim_thompson5910

here is one possibility
|dw:1433034550716:dw|

- jim_thompson5910

notice how it's the combination of two inequalities

- MeowLover17

So how would i write that as a system of inequalities??

- MeowLover17

I dont understand how to answer it :/

- jim_thompson5910

what two points lie above point E? ignore the other points A through F

- MeowLover17

(3,2) (3,3)

- jim_thompson5910

ok I'm going to toss out (3,3)
and replace it with (4,3)
that way we can draw a line through those two points. This line will be completely above point E

- jim_thompson5910

what is the equation of this line?

- MeowLover17

Okay.

- MeowLover17

y=x

- jim_thompson5910

nope

- MeowLover17

I know the slope goes up by 1, but im not sure of the y-intercept.

- MeowLover17

y=x-2

- MeowLover17

Is that the equation of the line?

- jim_thompson5910

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- jim_thompson5910

what is the equation of that green line?

- MeowLover17

y=x-1

- MeowLover17

am i wrong o-o

- jim_thompson5910

yep y = x-1

- jim_thompson5910

we want to shade below this line, so we could have y < x-1

- MeowLover17

Okay

- MeowLover17

So now i'm guessing we have to make another line with 2 points under A then shade where they overlap receiving the system of inequalities??

- jim_thompson5910

that is correct

- jim_thompson5910

something like this

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- MeowLover17

Indeed.

- MeowLover17

So could help me create the answer to part?

- jim_thompson5910

I'll brb, but I can do so when I get back

- MeowLover17

ok i'll be waiting here

- MeowLover17

Part A: So to graph the two lines first i must chose two points above points E, in this case i chose points (3,2) and (4,3), now i must draw the line going through these points and i should hit the y-axis at -1. Next i must choose two points under point A, so i choose (2,-4) and (3,-5) one i've drawn the line through these points i should hit the y-axis at -2. Now i must shade where both A, and E are within these instersecting lines. Which would be on the right side of this graph.
Equations= y=x-1 & y=-x-2

- jim_thompson5910

ok back
yes the two equations are y = x-1 and y = -x-2
the inequalities are y < x-1 and y > -x-2

- MeowLover17

Is that proper?

- jim_thompson5910

graphing both inequalities at the same time gives you the shaded region
|dw:1433036051038:dw|

- jim_thompson5910

proper? what do you mean?

- MeowLover17

@jim_thompson5910 Sorry i lost connection

- jim_thompson5910

thats ok

- jim_thompson5910

hopefully you see how I'm getting what I wrote above

- MeowLover17

Okay so i meant is my answer for Part A, okay?

- MeowLover17

Yea i understand.

- jim_thompson5910

they want inequalities, not equations

- jim_thompson5910

but the equations are useful in forming the boundaries

- MeowLover17

oh ok

- MeowLover17

So was my answer for part A feasible?

- jim_thompson5910

it's close to being complete

- MeowLover17

I put the inequalities under the equations part on my worksheet.

- MeowLover17

What else shall i add?

- jim_thompson5910

add in info about the inequalities and their shaded regions

- MeowLover17

Yea i did, but I'm not sure how to explain the "shaded" regions.

- jim_thompson5910

equation
|dw:1433036725634:dw|

- jim_thompson5910

inequality
|dw:1433036745339:dw|

- jim_thompson5910

the inequality includes the shaded region which extends forever downward and to the right (below the line y = x-1)

- MeowLover17

Okay i see the difference between an inequality and equation, for an inequality you must shade or make dashed depending on if its equal to or not but for an equation you just draw the line.

- jim_thompson5910

correct, I forgot about that part

- jim_thompson5910

since y < x-1 has no line under the < sign, we need a dashed boundary line

- MeowLover17

Yes

- jim_thompson5910

but you can easily make it \[\Large y \le x-1\]

- MeowLover17

Okay so let me show you my answer for part A:
Its the same as i showed above just with the inequalities underneath it because i don't know what more to explain.

- MeowLover17

This is for an online course so i can't draw graphs or anything i just type explanations :/

- jim_thompson5910

then do your best to describe the equations/graphs. So mention the points involved and the direction of the shading, and the boundary line type

- jim_thompson5910

|dw:1433036996621:dw|
this boundary line goes through (3,2) and (4,3)
it is a dashed boundary line (assuming you go with y < x-1)
the shading is below the boundary line

- MeowLover17

Okay let me explain it here then ill transcribe it.
Part A: Continuation - After graphing y-x-2, i shaded above it because when i test points below it does not work, now i can shade infinitley if i wanted too, but i am only shading where both shades meet from y>-x-2 and y

- MeowLover17

If i add that on to my first answer does it make it complete?

- jim_thompson5910

yes that wraps up part A

- MeowLover17

Okay now could you help me answer parts B and C???

- jim_thompson5910

Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A.

- jim_thompson5910

I'll show you how to verify point A and I'll let you verify point E

- MeowLover17

K

- jim_thompson5910

verifying point A
point A is (x,y) = (2,-3)
y < x-1
-3 < 2-1 ... plug in (x,y) = (2,-3)
-3 < 1 ... this is true
------------
y > -x - 2
-3 > -2 - 2 ... plug in (x,y) = (2,-3)
-3 > -4 ... this is true
-------------
since y < x-1 AND y > -x - 2 are true at the same time for the ordered pair (2,-3), this confirms that point A is indeed in the solution set of this system of inequalities

- MeowLover17

Oh i see so you just tested point A for both inequalities and it proved true.

- MeowLover17

Now i would have to do the same for E

- MeowLover17

right?

- jim_thompson5910

correct

- MeowLover17

Okay do i have to show this work or can i just explain it for part B?

- jim_thompson5910

showing work is always a good idea, but I guess you could explain it if you want. It will depend on how the teacher wants it

- MeowLover17

Okay ill just show your work for A then explain for E.

- MeowLover17

Okay now on to the final part C

- jim_thompson5910

Part C: William can only attend a school in his designated zone. William's zone is defined by y < -x - 1. Explain how you can identify the schools that William is allowed to attend.

- jim_thompson5910

so the goal here is to figure out which points (A through F) satisfy y < -x-1

- MeowLover17

oKAY

- jim_thompson5910

and you can use steps similar to what I had done in part B

- MeowLover17

Btw pOINTS a THROUGH f ARE SCHOOLS in a city

- MeowLover17

So do i just test all points in y>1-x to solve for c??

- jim_thompson5910

you mean y < -x-1, right?

- MeowLover17

Oh okay so my Answer for Part C would look like
Part C: William can only attend schools that satisfy his zone which is y<-x-1, to figure out which schools would satisfy this i must plug in points A through F into this inequality and see which are true, those that are true are schools that William can attend those that are false or don't make sense are those that he can not attend.

- MeowLover17

Is this correct???

- jim_thompson5910

so which points make y < -x-1 true?

- jim_thompson5910

you provided the explanation as to how to find the points, but I think they also want the points listed

- MeowLover17

It doesn't say that.

- MeowLover17

It says "Explain how you can Identify the schools that william is allowed to attend" Not list the schools

- MeowLover17

So does that mean my answer is correct???

- jim_thompson5910

yeah if they don't want the list, then you have it completed

- MeowLover17

Okay i have one more question could you help me on it??

- jim_thompson5910

ok

- jim_thompson5910

what's the question?

- MeowLover17

Oh, its like a whole other problem with parts a,b,c

- MeowLover17

Could you give me about 10 minutes or so, i just wanna transcribe the work on here to my worksheet.

- jim_thompson5910

alright

- MeowLover17

Thanks

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