Linear functions

[hot stump]

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[stiff fern]

Show your work for a.

[cinder tulip]

gimme a sec

all i did was this

i also found x which is 18

but i dont know where to go after this

i got c

[stiff fern]

"Found x which is 18"?

[stiff fern]

This isn't work.

[cinder tulip]

😔

sorry man

this

then i did 105 + 0(15)

[stiff fern]

Okay, stop.

What is the general form for the equation of a line?

[cinder tulip]

what do you mean

[stiff fern]

...I'm almost certain you must have been taught this.

[cinder tulip]

a donkey would teach better than my teachers

thats why im here

[stiff fern]

Okay.

So a line has an equation of the form y = mx + c.

[cinder tulip]

i see

[stiff fern]

We call m the slope or gradient, and c is the y-intercept.

[cinder tulip]

alright

[stiff fern]

Now, when we say that a curve has an equation, what we mean is that the curve is the set of all points (x, y) where the values of x and y make the equation true.

[cinder tulip]

okay

[stiff fern]

So looking here, we want an equation of the form w = md + c.

[cinder tulip]

i see

[stiff fern]

Stop.

[cinder tulip]

sorry

[stiff fern]

When it says "the average weight of a hen beginning the diet was 105g", what it's saying is that the point (0, 105) is on the line. It's saying 105 = 0m + c.

[cinder tulip]

yeah

[stiff fern]

And what can we learn from that equation?

[cinder tulip]

we can use it

[stiff fern]

...what does that equation tell us? The equation 105 = 0m + c?

[cinder tulip]

that y is 105?

[stiff fern]

Where is y?

I don't see a y, where do you see a y?

[cinder tulip]

i dont know

[stiff fern]

Okay. Well, let's just do some arithmetic. What's 0m?

[cinder tulip]

idk meters?

[stiff fern]

...no.

0m. 0 * m.

[cinder tulip]

oh

[stiff fern]

What is it?

[cinder tulip]

0?

[stiff fern]

Yes.

[cinder tulip]

🔥

[stiff fern]

And so 0m + c = 0 + c. What's 0 + c?

[cinder tulip]

c?

[stiff fern]

Yes.

Therefore: 105 = 0m + c 105 = 0 + c 105 = c

And so our line is y = mx + 105.

[cinder tulip]

alright

[stiff fern]

And that's actually why c is called the y-intercept. Because the line passes through the point (0, c).

[cinder tulip]

ok

[stiff fern]

So c is the y-coordinate of the point at which the line intercepts, or intersects, the y-axis.

[cinder tulip]

i see

[stiff fern]

So now, after 15 days, the hens weigh 375 grams.

[cinder tulip]

ah

i get you

[stiff fern]

NO. NO YOU DON'T.

[cinder tulip]

oh

[stiff fern]

STOP SKIPPING AHEAD.

[cinder tulip]

sorry

[stiff fern]

After 15 days, the hens weigh 375g.

This means the point (15, 375) is on our line.

Which means 375 = 15m + 105.

[cinder tulip]

alright

[stiff fern]

So do you know how to solve an equation?

[cinder tulip]

yes

[stiff fern]

Solve for m.

[cinder tulip]

105 - 375

270 = 15m

[stiff fern]

No.

[cinder tulip]

no?

[stiff fern]

No.

Other way around.

[cinder tulip]

you add them?

[stiff fern]

...you subtract them the other way around.

375 - 105 = 270. 105 - 375 = -270.

Subtraction is not commutative.

[cinder tulip]

oh my bad

i see

then uhh 15/-270?

[stiff fern]

Stop.

Okay, so you don't know how to solve an equation

Here's how it works.

We have an equation.

This equation is true.

Which means that m is a number with a value that makes the equation true.

We want to know what this value of m is.

We accomplish this by transforming this true equation into other true equations.

[cinder tulip]

ok

[stiff fern]

Equations that must be true if this equation is true.

[cinder tulip]

isnt it like solving for "x"?

[stiff fern]

Yes. Which I'm convinced you also don't understand.

[cinder tulip]

lool i do

[stiff fern]

I think you don't.

[cinder tulip]

youre right

[stiff fern]

Look.

It's okay not to know things.

My entire purpose here is to teach you things.

But it's hard to do that if you refuse to admit you don't know them.

[cinder tulip]

i lowky thought its you do -270/15 which gives m

[stiff fern]

Yeah, stop thinking like that.

[cinder tulip]

ok

[stiff fern]

It's not "you do [some random expression]".

It's you transform the equation.

[cinder tulip]

transform the equation?

[stiff fern]

Yes.

Here's the rules.

If: a = bThen: a + c = b + c a - c = b - c a * c = b * c a / c = b / cAnd also some other stuff you don't need right now.

We have 375 = 15m + 105.

How can we transform this equation to get closer to our goal, which is an equation of the form m = [some number with a known value]?

[cinder tulip]

using "a + c = b + c"?

[stiff fern]

What value of c?

[cinder tulip]

105

[stiff fern]

So 375 + 105 = 15m + 105 + 105?

[cinder tulip]

no

[stiff fern]

I mean, it does, but that's the wrong move, I agree.

[cinder tulip]

so whats the right move

[stiff fern]

Well, adding 105 to both sides doesn't make sense. What else can we do with 105 to both sides?

[cinder tulip]

minus it from both sides

[stiff fern]

375 - 105 = 15m + 105 - 105
270 = 15m```Huh, I think you're right.

So now what?

[cinder tulip]

😭

dividing?

[stiff fern]

Dividing what?

[cinder tulip]

270 by 15

[stiff fern]

Ah ah ah.

Both sides by 15.

[cinder tulip]

yes

[stiff fern]

270 / 15 = 15m / 15
m = 18```

[cinder tulip]

😭

[stiff fern]

It's m, not x.

[cinder tulip]

ignore it 😭

i still got 18

[stiff fern]

Now we know our linear equation is y = 18x + 105.

Or, in terms of w and d, w = 18d + 105

[cinder tulip]

yes

wait so i done it right before no?

[stiff fern]

Did you get an equation before?

[cinder tulip]

i used something like this

and the 375 is the same as the question gave

[stiff fern]

The problem is that you were just making things up.

[cinder tulip]

ur right i was

[cinder tulip]

so how do i solve the questions after getting the equations 😔