Question

http://prntscr.com/da8u5n
Help? :)

Answer 1

any ideas of the equations of the lines or how to find them

ignoring inequalities for now

Answer 2

Nope. I have no idea about this question...
I never really understood the concept of this... :(

Answer 3

see the attached image

where is point A located? Give an ordered pair

Answer 4

(0,2)

Answer 5

good, how about point B?

Answer 6

(2,1)

Answer 7

so we have one line through (0,2) and (2,1). Are you able to determine the slope using these two points?

Answer 8

Yes, give me a sec.

Answer 9

1/2

Answer 10

the slope should be negative. Why? Because as you move from left to right, you're going downhill

the slope is actually -1/2

Answer 11

-1/2 = rise/run

rise = -1
run = 2

the rise of -1 means we move down 1
the run of 2 means we move over 2

Answer 12

yesssss... :/
And where do we move 1 down and 2 right from which point?

Answer 13

from any point you want to get to the next point

so to move from A to B, you go down 1, then over to the right 2. You keep this pattern up to generate more points on this same line. If you started at B(2,1) and followed this pattern, then you'd get to (4,0) which is another point on this line.

Answer 14

Okay and then what do we do?
How do I answer the question? :/

Answer 15

are you familiar with y = mx+b form?

Answer 16

slope-intercept form, yes. :)

Answer 17

m is the slope
b is the y intercept

Answer 18

so you just found that m = -1/2 for that line through A and B

what is the value of b? What is the y intercept of that line?

Answer 19

2

Answer 20

m = -1/2 and b = 2

so we'll just do two replacements to go from
\[\Large y = mx+b\]
to
\[\Large y = -\frac{1}{2}x+2\]
agreed?

Answer 21

Yes, sir!

Answer 22

that's the boundary line equation through points A and B. Where is the shaded region in relation to this boundary line? Is it above the boundary line? or below the boundary line?

Answer 23

Above?

Answer 24

yes, if you started at say point A, moving up leads you to the blue shaded region. Moving down gets you to the nonshaded region

Answer 25

yuh huh:)

Answer 26

so because the shaded region is above the boundary line, we will have a "greater than" symbol for the inequality sign

the boundary is solid, so we have "or equal to" thrown in as well

That means
\[\Large y = -\frac{1}{2}x+2\]
will turn into
\[\Large y \ge -\frac{1}{2}x+2\]

Answer 27

make sense?

Answer 28

Yep
So far so good :)

Answer 29

so that will go in one of the boxes. That's one of the inequalities

Answer 30

I'll let you try out the other inequality. Post your steps along the way (such as the slope, y intercept and things like that)

Answer 31

Hmm, okay... ugh, here goes
can you just probably tell me a new set of points just to start me off?

Answer 32

the other boundary line is the dashed line which goes through points B and C

Answer 33

2/1 is the slope

Answer 34

1 is the y intercept

Answer 35

or just 2, good

Answer 36

1 is not the y intercept

Answer 37

look where this dashed line crosses the y axis

Answer 38

ohhh -3

Answer 39

yep

Answer 40

so what is the boundary equation? I'm asking for the equation in y = mx+b form

Answer 41

y=2x+-3

Answer 42

which simplifies to y = 2x-3, good

Answer 43

how about the inequality?

Answer 44

Oh wait!
There isn't an inequality? :/

Answer 45

okay lol wait

Answer 46

the boundary will lead to the inequality

Answer 47

let's say you're at point C. How can you get to the blue shaded region? you have 2 moves: go up or down

Answer 48

up

Answer 49

so we'll have what as our inequality sign?

Answer 50

Greater than or equal to? :D

Answer 51

no "or equal to" because the line isn't solid. A dashed line means we don't have "or equal to"

Answer 52

So the boundary line
\[\Large y = 2x-3\]
leads to this inequality
\[\Large y > 2x-3\]

Answer 53

okayyyyy i somewhat get it now
so that means my inequality will be y > 2x+3

Answer 54

Why minus 3? :/

Answer 55

because adding a negative is the same as subtraction

Answer 56

y = mx+b
y = 2x + (-3)
y = 2x-3

Answer 57

We're adding a negative? :/

Answer 58

if it was +3, then the y intercept would be higher

Answer 59

Ohhhh!!!

Answer 60

Okay, wow!
Thank you so much for helping me!! :)
May you help me with one more?

Answer 61

sure, make a new post to avoid clutter