Satisfy the inequalities

[mental compass]

Please someone save me I’m gonna get an hour detention If it’s not done by tmr

<@&791435371564892232>

[slim wadi]

use y = mx + c

to find the equation of the lines

[graceful shadow]

The solid line has a grad of 2 and passes through 1 so it has an equation of 2x+1
the dottedline has grad of -1 and passes throuh 5 so it has an equation of -x+5
For the inequality to be satisfied it must be above the dotted and below the solid line

[mental compass]

I got these three equations:

1. x=4
2. y= -2x +12
3. y= x + 3

But I don’t know how to find them as inequalities bc the video doesn’t explain it very well

For this question btw

[scarlet sphinx]

the question is asking for what inequalities define the unshaded region

if the line is a full one, it is ≥ or ≤

if it's a dotted line the inequality is exclusive so < and >

the x coordinates for the unshaded region are all less than 4

so the 1st inequality is x≤4

then for y = -2x + 12

the unshaded region is "above" the line so it's greater than or equal to:
y≥ -2x+12

then for y=x+3 the unshaded region is below the line, so it's
y<x+3

does that look correct?

icl im not too sure myself lolt

[mental compass]

So when u form the equations, do u just have to look at where the lines are positioned to see what number they cannot be greater than or smth?

Bc this is a lot too process lol

[mental compass]

Lemme check

Ayy it was

[scarlet sphinx]

yeah if you think about it which inequality would make the unshaded area correct

[mental compass]

Ah I see

[mental compass]

So for this one I got the equations
y= -x + 5
and
y= 2x+1

Now I needa find out which inequalities satisfy correctly

So @scarlet sphinx would it be on this graph that the numbers cannot be bigger than 3.5?

Or have I got it wrong

[scarlet sphinx]

oh

let me check

make ur inequalities

like put it in the form y > ....

or y < ...

[mental compass]

That’s what I’m stuck on rn…

I still don’t get it ngl

[scarlet sphinx]

ok so in the question again its asking for the unshaded region

so it must be greater then the y= -x+5, and less than y=2x+1

so the inequalities would be

y> -x+5
y<= 2x+1

where <= means less than or equal to

[mental compass]

Wait did u just check if it was a dotted or solid line

To work it out

[scarlet sphinx]

huh no, whether the line is dotted or not tells you if the inequality is inclusive or exclusive

idk im prob explaining this well enough but basically you look whether the indicated region is "below" or "above" the line

[mental compass]

ah ok dw

[mental compass]

were these the final answers?

bc on my thing it giving different stuff

[scarlet sphinx]

oh they rearrange it

sideeye

[mental compass]

lol

[scarlet sphinx]

umm in that case it would be y+x>5

and y<=2x+1

i think

[mental compass]

alrighty il try it

[scarlet sphinx]

go onto https://www.desmos.com/calculator

it shades IN the inequality

y>=2x

so bc y is "greater than", the inequality is "above the line"

[mental compass]

Lemme see

What numbers did u insert

[mental compass]

Ohh ok

[scarlet sphinx]

i did y>=2x

[mental compass]

If it was less than it would be the oppsoue?

Opposite?*

[scarlet sphinx]

thats for y<=x

[mental compass]

I see

[scarlet sphinx]

wait

let me show u a diff example

[mental compass]

Alr

[mental compass]

Wait so is that bc its a negative?

[mental compass]

Oh wait nvm

[scarlet sphinx]

no the negative just changes the gradient of the line

so one line goes down and the other goes up

try using desmos a bit

it's good for understanding anything to do with graphs

[mental compass]

Ye I probably should tbh

Anyways tysm for the help u a life saver lol

Would’ve been sitting a 1 hr on Friday if I didn’t complete that

[scarlet sphinx]

ywww im sorry about the bad explanation 😭

[mental compass]

No u actually kinda helped me with it lol

[scarlet sphinx]

maybe someone else can give u a better one

[scarlet sphinx]

ah okk

[mental compass]

U addressed some misconceptions I had

Good teaching fr

Anyways I’m done lol, byee