Question

Hey, can someone explain to me how to write an inequality of this graph?

Answer 1

you can start by writing the equations of both intersecting lines. in both cases, the given region is above both lines.

Answer 2

are you with me king?

Answer 3

Not exactly, just started learning this so I admit to sucking..

Answer 4

lol. appreciate the honesty.

Answer 5

ok. lets start with the boundary of this graph. there are two intersecting lines. What we also need to know is whether or not the lines are solid or dotted. Solid boundary lines are written as a > or = to or < or = to. so far so good? tell me if it is not. questions are good

Answer 6

dotted lines are represented by strict inequalities such as just > or just <. no =. ok?

Answer 7

Okay, I think I get that.

Answer 8

okeedokee. now tell me, can you determine the equations of the two intersecting lines that close off that region?

Answer 9

It's dotted so it's < or >

Answer 10

good. now can you tell me the equations of both lines as if they were solid? bear with me here.

Answer 11

Not entirely sure how to get what the equations are just that it's < = and > =

Answer 12

can you tell me the slope of the line that crosses the y axis?

Answer 13

.I know m=(y2-y1)/(x2-x1) but I still get confused as to how to determine that from a graph

Answer 14

(I just started learning this yesterday sorry
)

Answer 15

nothing to worry about. i started this two days ago..

Answer 16

i am teasing :)

Answer 17

dont worry, you'll get through this just fine.

Answer 18

so lets start with finding the slope given a graph

Answer 19

always start where the line intersects the graph paper in exact coordinates, like (0,0) or (7,1). we dont want to try to approximate the slope if we dont have to.

Answer 20

so, for the line that intersects the yaxis, i would like you to look at the point (0,6) where it actually does intersect the y axis. lol

Answer 21

so far so good? scream if the pain gets too intense. :)

Answer 22

Lol yeah I got ya so far.

Answer 23

now, starting where the line intersects (0,6), move to the right one unit and tell me: does the line move up or down from that point? and if so, how far?

Answer 24

It moves down the y axis 5 and across the x to 5.

Answer 25

riiight. nice.

Answer 26

ok. a rule of thumb. if you move one unit to the right and the line drops, then it has a negative slope. if you move one unit to the right and the line rises, then it has a positive slope.

Answer 27

now, you also said that you moved over +1 units to the right and -1 units down. this translates to y2-y1=-1 and x2-x1=+1. this is the crux of reading graphs. so if you have questions, ask them now.. :)

Answer 28

this also means that the slope of the line is-1/+1=-1

Answer 29

seeing slope on a graph takes some practice. so don't feel upset if you are not seeing this immediately.

Answer 30

I suppose that makes sense...(Thanks so much for the patiences btw)

Answer 31

we all had to learn this at one time or another, and someone was patient with us once. :)

Answer 32

so, whether we like it or not, we have the slope, which is -1. we also have the y intercept, which is (0,6). so, can we get the equation of this line in order using the slope intercept form of a linear equation?

Answer 33

Yea y = mx + b right?

Answer 34

very nice. yes! so, our line has the equation.... (drum roll)

Answer 35

5=-1(5) + b

Answer 36

Trying to do this off of memory from seeing it so srry if I get something mixed up.

Answer 37

we should have something with an x and a y here.

Answer 38

we have m=-1 and we have b=6. now just substitute them directly into y=mx+b.

Answer 39

you are doing fine for your first day ;)

Answer 40

Was I right with the first part of it I got? 6=-1(5)+6

Answer 41

you are solving for the coordinates of a point on the line. I was asking for the general equation of the entire line. the difference is crucial to this problem. you need the equations of both lines to determine the inequalities that create the boundaries of the above region.

Answer 42

so, in this case, the equation of the line is going to be y=-x+6.

Answer 43

and if you look at the graph, you see that the region is above the line, so the inequality that represents the region above the left line is y> or =-x+6. now questions about doubts are really good here. :)

Answer 44

So if the line is shaded below then you get y<=x?

Answer 45

yes, you got it. also, the equals sign indicates that the line is solid and included in the region. dashed means it is not included in the region. ok?

Answer 46

Alright, pretty straight forward..Also since it's dotted and not solid it is y>-x+6 without = right?

Answer 47

you got it. nice. for me, it is really hard to see whether it is dotted or solid. there is no resolution in the drawing.

Answer 48

now, on to the next one.

Answer 49

take a straightedge if you have one, and extend the line on the right through the y axis

Answer 50

please tell me when you have done this...

Answer 51

It's -4

Answer 52

what a coincidence!!! that s what i got...

Answer 53

now, tell me. of what significance is -4?

Answer 54

what is -4 called?

Answer 55

It's our next y point right?

Answer 56

hint: it has to do with y=mx+b

Answer 57

So is it the y?

Answer 58

nope, it is the y intercept.

Answer 59

in y=mx+b, which is the y intercept?

Answer 60

b?

Answer 61

yes. so now we have y=mx-4. see how that works?

Answer 62

after that, we just find m and we are almost done

Answer 63

yeah :D

Answer 64

now, starting at the y intercept of -4, move over one unit. do you have to go up or down? and how many units do you go up or down?

Answer 65

just like we did the last line to find the slope

Answer 66

any ideas? guesses? inquiries? operators are standing by. :P

Answer 67

Sorry computer froze. Up 2 right?

Answer 68

sok.. noproblem. up 1. so tell me the slope. dont worry. i am walking you through this so that you will feel much better about the next one. :)

Answer 69

so if y2-y1=1 and x2-x1=1, what is the slope?

Answer 70

Thanks so much. And I guess slope is 1 since m=(y2-y1)/(x2-x1

Answer 71

you bet. now you have the equation of the line because you have the m and the b of y=mx+b

Answer 72

so.... drum roll.... what IS the equation of the line??

Answer 73

he whispers... no pressure

Answer 74

6>1x+-4 (for the x we keep the - like before right?)

Answer 75

not 6, but y. remember, it is y=mx+b. we had m=1 and b=-4. so we make a direct substitution and get y=1x+-4 or y=x-4.

Answer 76

now, we have the equation. is the region above or below our beloved line? and is the line dashed or solid?

Answer 77

this will lead us to our second and final inequality.

Answer 78

It is dotted and above the line so it's a negative.

Answer 79

hmmm.... what is negative?

Answer 80

dotted implies a strict inequality sign. and above means greater than

Answer 81

so use the equation of the line you have to write the inequality that does not include the line in the region

Answer 82

just like we did with the other line.

Answer 83

You mean y>-x-4?

Answer 84

*or y>x-4

Answer 85

yes, totally!! now that you have both lines (called a system), you have the equations of the region in the drawing.

Answer 86

you are done here with this problem. it has been a pleasure. unfortunately, i must go now. I hope this has helped some.

Answer 87

It has quite a lot. Thanks so much!

Answer 88

you are welcome. take care. bye