Question

Graphing inequalities help? Image included

Answer 1

Are you trying to answer for the green region or the yellow?

Answer 2

idk whatever the question asks i guess

Answer 3

The question you sent doesn't say. Let's assume its the green. Start by finding the equation for the dotted line....

Answer 4

it's both green and yellow because there's 2 equations. right?

Answer 5

Yes, one of the equations cuts the plane in half, and the other cuts it in half again

Answer 6

huh?

Answer 7

The first equation(line) divides the graph into two part, the green-yellow part and the unshaded part. The second equation(line) divides the green part from the yellow part

Answer 8

okay what does that have to do with finding the equation?

Answer 9

one of the equations you need is the equation of the line that separates the shaded part from the unshaded part. The other is the equation of the line that separates the green from the yellow.

Answer 10

oh

Answer 11

So start by finding the equation for the dotted line that divides yellow from green

Answer 12

yeaahh, I don't know how.. /:

Answer 13

OK. Can you find the y-intercept from the graph?

Answer 14

look for the point where the line goes thru the y-axis

Answer 15

3?

Answer 16

you got it. Let's call that number b. Now can you find the slope of the line?

Answer 17

idk what the slope is

Answer 18

Slope tells you how steep the line is and whether it slants up or down. To find it's value,
we need to find two points on the line. We have one, x=0 y=3, that you just found. Now follow the line until it hits the x-axis, what number is there?

Answer 19

Indeed, fwizbang is correct, the higher the slope's #, the steeper it is.

A slope of 2 means for every 2 units change in height (y-axis coordinate here) you go side-to-side only one unit. A steeper slope like a high-sloped roof.

A slope of 1/2 would mean for ever 1 unit change in height, you'd go 2 units side to side. A shallower slope like you might have on a road (26.565\(^o\ in fact I believe).

Answer 20

\[26.565^o\]

Answer 21

you guys are confusing me -_______-

Answer 22

Sorry. We were trying to find the equation of the dotted line in your picture, right?
One way to do that is to find its y-intercept(3), and its slope.....

Answer 23

okay, i got that, now how do we find the slope?

Answer 24

why can't we just do the substitute thing like the last one

Answer 25

To find the slope, we're going to find two points on the line, and then divide the change in y(the "rise") by the change in x(the "run"). So we need to find the x and y values for a second point on the line. An easy one to use ids the pint where the line hits the x-axis(the "x-intercept").

Answer 26

In the last one, we had the equations and were trying to find the picture. Here we have the picture, and are trying to find the equations

Answer 27

the one before that, where there was a picture also you said something about substituting

Answer 28

We can't substitute if we don't have an equation to substitute into.

Answer 29

We're almost there, can you find the pint were the line hits the x-axis?

Answer 30

3

Answer 31

Good. Now we have two points, the first had x=0 and y=3, and now the second has
x=3 and y=0. So we're going to find the slope by finding the rise, which is the change in the y's

rise = (2nd y) - (first y) = 0 - 3 = -3

and dividing it by the run, which is the change in the x's,

run = (2nd x) - (first x) = 3 - 0 =3

so that the slope = rise/run = -3/3 = -1.

Still with me?

Answer 32

no you lost me

Answer 33

Ok. do you have the coordinates of the two points?

Answer 34

3 and -1?

Answer 35

not quite. Remember the first point was where the line went thru the y-axis, so it had x=0
and y=3.

Answer 36

the second point was where the line went thru the x-axis, so it had y=0 and x=3.
(all these 3's can be a little confusing.)

Answer 37

0 and 3 aren't in my answer choices.. so it's D?

Answer 38

patience, we still have a little more to do

Answer 39

We have two points on one of the lines, we need to find its equation

Answer 40

:(((((((((((

Answer 41

I'm sorry, but we can get thru this if we keep at it.....Can you find the change in the y's?(the rise)

Answer 42

if i knew how.

Answer 43

The first point,where the line went thru the y=-axis, had y=3. The second point,
where the line went thru the x-axis, had y=0. Subtract the first y from the second

Answer 44

-3

Answer 45

Great, that's the "rise". Now do the same thing for the x's. The first point had x=0, the second had x=3. So, the "run" is ?

Answer 46

3

Answer 47

Perfect. Now to find the slope, take the rise and divide it by the run

Answer 48

1

Answer 49

Almost, the rise was -3 and the run was 3....

Answer 50

-1

Answer 51

There you go. So the slope of the line is -1. Since the slope is negative it tells us that as
we move to the righth in the ppicture, the line goes down. The -1 says that for every step we go to the right, the line goes one step down......

Answer 52

Theres a rule that says we can find the equation of the line by

y = (slope) times x + y-intercept

or, if slope = m, y=mx +b

Answer 53

Remember the first thing you found was the y-intercept(3), So the equation for our line is ?

Answer 54

3=mx+b?

Answer 55

not quite, we want to keep the y and the x, but substitute for the slope(m) and the y-intercept(b)....

Answer 56

rember that the y-intercept(b) was 3 and the slope(m) was -1

Answer 57

y=-1x+3?

Answer 58

Perfect. So now we have the first equation we need (y=-x+3). Already we can rule out answer a, right?

Answer 59

yeah

Answer 60

So now we need to find the equation of the line that separates the shaded and unshaded regions. Remember how this works:

1) We need to find two points on the line.
2)The first easy point to find is the point were the line goes thru the y-axis. It has x=0, and its y-value(which we read off the picture) is the y-intercept(b) that appears in the equation of the line.
3) The second easy point to find is where the line hits the x-axis. It has y=0 and its x-value
we can get off the picture.
4) To find the slope(m) , we find the change in the y-value(the rise) and divide it by the change in the x-values(the run)
5) the equation for the line is y=m x +b.

The importtant thing is to remember that you just need to do this one step at a time, not all at once, so start with 1 and work your way down. Wanna give it a try?

Answer 61

that's SO much work, plus i have another harder question after this :/ is there an easier way?

Answer 62

Every time you do it, it'll be quicker and easier, until you won't even have to think about it anymore, Can you try step 2?

Answer 63

i thought we already did those steps

Answer 64

We did, but now we need to do it for the second line so we can get the second equation we need.

Answer 65

-.-

Answer 66

Hang in there, we're going to get this. Can you find the point were the second line hits the y-axis?

Answer 67

it doesn't

Answer 68

oh wait, -2

Answer 69

There you go. That tells us that the y-intercept(b) is -2. Now find the point where
the line hits the x-axis.

Answer 70

1

Answer 71

great. So we have the two points we need x=0, y=-2, and y=0, x=1. We're ready for step 4. What are the rise and the run?

Answer 72

-3 and -3?

Answer 73

aThat was for the first line, we're working on the 2nd now. remember that

rise =2nd y - first y

run = 2nd x- first x

Answer 74

This is pointless -.- I don't understand what i'm doing and I don't know how to do this and I have 3 other quizzes to do.. This is just hopeless !

Answer 75

I'm sorry your frustrated. We're trying to find the equations for the two lines
that appear at the edges of the green region so we can pick out the answer.
We already have one, so if we can find the equation for the other we'll be essentially done.

Answer 76

ughhhhh. how do we do the rise & run

Answer 77

Here's a different thing to try. On the picure, start at the first point and count hoe many boxes you have to go sideways to get to the second one.

Answer 78

no id rather do it the way we did it last time, if that's okay?

Answer 79

ok. then take the first x(0), and subtract it from the 2nd x(1) to get the run.

Answer 80

1

Answer 81

thats the run. Now find the rise = 2nd y - first y

Answer 82

what were they again?

Answer 83

the 2nd y was 0, because the point is on the x-axis. The first y was the y-intercept(b), which was -1

Answer 84

opps, -2

Answer 85

so it's -2

Answer 86

?

Answer 87

Sorry, I had to take care of something else for a bit. 0 -(-2) = 2. So the rise is 2 and the run is 1. The slope is the rise/run =?

Answer 88

2

Answer 89

the equation for the line is y = m x +b, where m is the slope and b the t-intercept,
so we get.....

Answer 90

y=2x+b ( i don't know what goes in place of b )

Answer 91

b is the y intercept, which was -2 in this case, so y=2x-2.

Answer 92

Hopefully, the 2nd time was a little easier(humor me), but the good news is that the hard part is done. We have the two equations we need

y = -x + 3 and y =2x-2

the code in these pictures is that when a line is dotted, then the points on the line
aren't part of the solution, so the = sign in the equation gets replaced with either a <
or a >. When the line is solid, the points on the line are part of the solution, so the = is
replaced by a >= or a <=. So the answer we want either has

y< -x+ 3 or y>-x+3 and y>= 2x -2 or y<= 2x-2.

To figure out which, we just have to pick any point in the green regionof the picture,
say y=0 x=4, and substitute it in like we did before.....

Answer 93

substitute where?

Answer 94

into the inequalities. If the inequality is true after you substitute, then its one of the two we want

Answer 95

-______-

Answer 96

so if y=0 and x=4, is y< -x +3 correct?