Question

Help, can anyone work through this with me?. I only need help with part A

Answer 1

@jim_thompson5910

Answer 2

Just part A is all I need help with

Answer 3

You don't need a system of inequalities. You just need one inequality to capture points B and C

Answer 4

What is the x coordinate of either point?

Answer 5

infact you don't even need an inequality, you just need an equation.

Answer 6

But why did they say create a system of inequalities? @jim_thompson5910

Answer 7

I think you should just do it using 2 inequalities, because it seems to be an exercise to practice graphing them.

Answer 8

What you need to do is find two lines, one above both points and one below both. Get those equations.

Answer 9

They can be ANY lines, so long as one is above BOTH and one is below BOTH

Answer 10

then you need to relate the lines to the points themselves, so for the line above, instead of an equation (like you would normally have for a line) use an inequality to set a region (for example, if the line is above both points, you would use y<mx+b)

Answer 11

do the opposite for the line below, then solve the system to show they fit.

Answer 12

Can you show me what you mean? @sylbot i'm a more visual learner

Answer 13

ok give me a second to graph this

Answer 14

oh i made a small error, they can't be ANY lines, when combined they must isolate B and C

Answer 15

ehh ok.

Answer 16

http://i.imgur.com/sZQ0ivO.png

So you see the lines I drew? you would get something similiar to that, nicer equations ofc, and set one as y>mx+b and the other to y<mx+b

Answer 17

let me draw better ones if you don't understand.

Answer 18

Okay and can you work with me to get the inequalities.. i'm not good at creating them @sylbot

Answer 19

http://i.imgur.com/aBV3Y97.png

Answer 20

ok so you see the two lines? what are they equations (I made these easier). Give me the slope intercept form for both.

Answer 21

y=mx+b

Answer 22

no for the exact lines I drew. You can see the coordinate plane and find the actual slopes and intercepts.

Answer 23

ugh I suck at this :( I feel dumb

Answer 24

haha dw, ill mark it up some more one sec, this will make it easier.

Answer 25

Like I see the point of intersection which is (0,-1)

Answer 26

http://i.imgur.com/X5eSZQC.png

Answer 27

I've color coded some points on the lines, now can you give me the equations? You can use point-slope form and convert if you need to.

Answer 28

also the (2,-4) is blocked out :P but its a -4

Answer 29

Ok so i can pick any of these points, find the slope then use point slope form?

Answer 30

wait nevermind that question

Answer 31

yeah just give me the equations, and I can help you get inequalities super easy after that.

Answer 32

Ok for the red line I got y=2x-1

Answer 33

I'm working on the green line now

Answer 34

good job with the first one!

Answer 35

I'm kinda struggling with the green line. I have it in point slope form\[y--1= -3/2(x-0)\] I need help simplifying that

Answer 36

so I see it'll be \[y+1= -3/2x+0\]

Answer 37

thats correc,t just add 1 to both sides to get slope intercept form

Answer 38

ok got it, \[y= -3/2x+1\]

Answer 39

so now that you have the equations of both lines, you have to determine the region you want. So the line itself represents y values that are exactly equal to that function of x.

Answer 40

to say you want all points below a line you'd set y LESS THAN that function, so it would look like

y<-3/2-1

Answer 41

oh whoops, I said add one, I meant subtract (Small oversight its np)

Answer 42

But for the GREEN line you want every y value ABOVE the line so actually the answer would be
y>-3/2x -1

Answer 43

do you understand how it works? When you want a region below a line, you can represent it by saying "Instead of having y EQUAL TO a function of x, I'll set it Less than that same function".

Answer 44

when you want a region ABOVE a line, you can represent it by saying "I won't set y equal to a function of x but GREATER than a function of x"

Answer 45

but how would I know with just those equations, what would the inequality sign be?

Answer 46

so lets review really quickly, what are the two equations (and for which line)

Answer 47

The red line: y=2x-1
Green line: \[y= -3/2x+1\]

Answer 48

ok, so where are B and C in relation to the red line.

And then in relation to the green line.

Answer 49

in terms of Y values,

Answer 50

Sorry to barge in, but here is another way to solve the problem. There are infinitely many ways to do this since you can move the boundary lines around and add new regions to overlap. Anyways, have a look over it but I recommend that you stick to sylbot's method you're doing now because you're nearly finished with it.

Answer 51

^^ that is completely correct, like I said you can have ANY lines so long as the two points are isolated.

Answer 52

I just gave you an example of two non vertical lines because I thought you would benefit from and example with non vertical lines, since part c is like that.

Answer 53

So the equations that Jim gave me is actually the answers?

Answer 54

they are one possible set of answers

Answer 55

oops typo lol

not system of equations...I meant to say "system of inequalities"

Answer 56

sylbot's answer is another possible answer. There are infinitely many ways to answer this

Answer 57

thats correct, I like his graph a lot :D, but I do think you could benefit from looking at an example of a nonvertical line

Answer 58

okay i'll finish sylbot inequalities because like you said earlier because i'm almost finished

Answer 59

ok so where are points B and C in relation to the Red line. Are they above or below? (this is generally how we describe position when using y and a function of x )

Answer 60

don't think about left and right, just are they above or below.

Answer 61

The red line is above and the green line is below?

Answer 62

haha ok so the points themselves are BELOW the red line correct? (since the line is above)

Answer 63

this means that instead of expressing the points where y EQUALS 2x-1, we want anything below that as well.

Answer 64

so to say this, we use the inequality,
y<2x-1

This expression shows that we want every y value below 2x-1, thus expressing the entire region below the line.

Answer 65

Okay and for the green line the points are above

Answer 66

you can see from my crude drawing what I region I mean.
http://i.imgur.com/Amfhn3S.png

Answer 67

yeah so for the green line you'd want everything above.

so you'd do

y>-3/2x -1

Answer 68

here is another crude drawning of the green region.
http://i.imgur.com/48Wi9tn.png

Answer 69

so to get both points isolated, you use a system of inequalities (just like jim said) to get the region common to BOTH.

Answer 70

Okay so when I explain it.. the red line has shading below and the green line has shading above.

Answer 71

will they have any overlapping shading?

Answer 72

@sylbot

Answer 73

yes
here is the overlap
http://i.imgur.com/Oe51IFV.png

Answer 74

As you can see, the two points are isolated.

Answer 75

so the system would be
y>-3/2x-1
y<2x-1

Answer 76

Ok I see and I understand. Thanks so much. I really really appreciate it :)

Answer 77

and thanks to you as well @jim_thompson5910

Answer 78

lol I wish I had better pictures, I hope you understood anyways.

Answer 79

No I do and your pictures were fine