Hey Z4 Got any input??
So what do i answer for part A?
Like where is the system of inequalities or how do i make it???
Jim please help
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)
here is one possibility |dw:1433034550716:dw|
notice how it's the combination of two inequalities
So how would i write that as a system of inequalities??
I dont understand how to answer it :/
what two points lie above point E? ignore the other points A through F
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
what is the equation of this line?
I know the slope goes up by 1, but im not sure of the y-intercept.
Is that the equation of the line?
what is the equation of that green line?
am i wrong o-o
yep y = x-1
we want to shade below this line, so we could have y < x-1
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??
that is correct
So could help me create the answer to part?
I'll brb, but I can do so when I get back
ok i'll be waiting here
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
ok back yes the two equations are y = x-1 and y = -x-2 the inequalities are y < x-1 and y > -x-2
Is that proper?
graphing both inequalities at the same time gives you the shaded region |dw:1433036051038:dw|
proper? what do you mean?
@jim_thompson5910 Sorry i lost connection
hopefully you see how I'm getting what I wrote above
Okay so i meant is my answer for Part A, okay?
Yea i understand.
they want inequalities, not equations
but the equations are useful in forming the boundaries
So was my answer for part A feasible?
it's close to being complete
I put the inequalities under the equations part on my worksheet.
What else shall i add?
add in info about the inequalities and their shaded regions
Yea i did, but I'm not sure how to explain the "shaded" regions.
the inequality includes the shaded region which extends forever downward and to the right (below the line y = x-1)
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.
correct, I forgot about that part
since y < x-1 has no line under the < sign, we need a dashed boundary line
but you can easily make it \[\Large y \le x-1\]
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.
This is for an online course so i can't draw graphs or anything i just type explanations :/
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
|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
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
If i add that on to my first answer does it make it complete?
yes that wraps up part A
Okay now could you help me answer parts B and C???
Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A.
I'll show you how to verify point A and I'll let you verify point E
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
Oh i see so you just tested point A for both inequalities and it proved true.
Now i would have to do the same for E
Okay do i have to show this work or can i just explain it for part B?
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
Okay ill just show your work for A then explain for E.
Okay now on to the final part C
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.
so the goal here is to figure out which points (A through F) satisfy y < -x-1
and you can use steps similar to what I had done in part B
Btw pOINTS a THROUGH f ARE SCHOOLS in a city
So do i just test all points in y>1-x to solve for c??
you mean y < -x-1, right?
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.
Is this correct???
so which points make y < -x-1 true?
you provided the explanation as to how to find the points, but I think they also want the points listed
It doesn't say that.
It says "Explain how you can Identify the schools that william is allowed to attend" Not list the schools
So does that mean my answer is correct???
yeah if they don't want the list, then you have it completed
Okay i have one more question could you help me on it??
what's the question?
Oh, its like a whole other problem with parts a,b,c
Could you give me about 10 minutes or so, i just wanna transcribe the work on here to my worksheet.