Recognizing Linear Functions

Algebra

Graphing points, equations and inequalities

Graphing solutions to equations

Ordered pair solutions of equations
Ordered Pair Solutions of Equations 2
Plotting (x,y) relationships
Graphs of Linear Equations
Application problem with graph
Ordered pair solutions to linear equations
Interpreting Linear Graphs
Exploring linear relationships
Recognizing Linear Functions
Identifying linear relationships

Additional content

Graphing lines 1

Recognizing Linear Functions Recognizing Linear Functions

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Recognizing Linear Functions

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Deirdre sedang menyelesaikan pasalah fungsi yang mengandungi
titik titik tersebut
ini adalah nilai x manakala ini pula nilai y
soalan meminta, adakah fungsi ini fungsi linear atau fungsi bukan linear ?
jadi fungsi linear, cara untuk mengenalpasti ia adalah dengan melihat
perubahan dalam x adalah sama dengan
perubahan dalam y
sebangai contoh, perubahan dalam setiap 1 nombor dalam x,
adakah y akan selalu bersamaan dengan 3 ?
ataupun adakah ia selalu bersamaan dengan 3 ?
jika nilainya sama, maka anda tahu ia adalah
fungsi linear
jika untuk setiap perubahan dalam x-- jadi disini x sentiasa bertambah
dengan 1, jika x sentiasa bertambah dengan 1,
y juga harus sama
jika nilai y tidak sama, anda sudah pastinya tahu ia adalah
fungsi bukan linear
saya boleh tunjukkan di sini
jika perubahan dalam x --kita akan guna nombor yang berbeza
jika ini pergi dari 1 ke 2 & kemudian 2 ke 4-- apa yang anda harus buat adalah
bahagikan perubahan dalam y dengan perubahan dalam x dan
itu tidak boleh diubah
untuk tidak kelirukan anda, biar saya tuliskan di sini
jika sesuatu itu adalah linear , perubahan dalam y per
perubahan dalam x tidak boleh diubah
sekarang dalam contoh ini, perubahan dalam nilai nilai x
adalah sentiasa bertambah dengan 1 kan ?
kita pergi dari 1 ke 2, 2 ke 3, 3 ke 4, 4 ke 5
jadi dalam contoh ini, perubahan dalam x akan sentiasa bertambah dengan 1
jadi untuk menjadikan fungsi ini menjadi linear, perubahan dalam y
perlu tidak diubah kerana kita akan ambil ia dan
bahagikan dengan 1
mari kita lihat jika perubahan dalam y kita adalah sama
bila 11 ke 14, ia bertambah 3
bila 14 ke 19, ia bertambah 5.
jadi saya sudah nampak bahawa nilainya tidak konsisten
ia tidak bertambak 3 sebaliknya bertambah 5
dan disini, kita bertambah sebanyak 7
dan disini, kita bertambah sebanyak 9
So we're actually going up by increasing amounts, so we're
definitely dealing with a non-linear function.
And we can see that if we graph it out.
So let me draw-- I'll do a rough graph here.
So let me make that my vertical axis, my y-axis.
And we go all the way up to 35.
So I'll just do 10, 20, 30.
Actually, I can it do a little bit more granularly than that.
I could do 5, 10, 15, 20, 25, 30, and then 35.
And then our values go 1 through 5.
I'll do it on this axis right here.
They're not obviously the exact same scale, so I'll do
1, 2, 3, 4, and 5.
So let's plot these points.
So the first point is 1, 11, when x is 1, y is 11.
This is our x-axis.
When x is 1, y is 11, that's right about there.
When x is 2, y is 14, that's right about there.
When x is 3, y is 19, right about there.
When x is 4, y is 26, right about there.
And then finally, when x is 5, y is 35, right up there.
So you can immediately see that this is not
tracing out a line.
If this was a linear function, then all the points would be
on a line that looks something like that.
That's why it's called a linear function.
In this case, it's not, it's non-linear.
The rate of increase as x changes is going up.

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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

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When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...

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At 2:33, Sal says "double bonds" but should say "single bonds."

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