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## 8th grade

### Course: 8th grade > Unit 3

Lesson 13: Linear and nonlinear functions- Recognizing linear functions
- Linear & nonlinear functions: table
- Linear & nonlinear functions: word problem
- Linear & nonlinear functions: missing value
- Linear & nonlinear functions
- Interpreting a graph example
- Interpreting graphs of functions
- Linear equations and functions: FAQ

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# Linear & nonlinear functions: table

Learn to determine if a table of values represents a linear function. Created by Sal Khan.

## Want to join the conversation?

- what if the table can be both linear and nonlinear?. thank you(7 votes)
- There are only two possibilities there. Either the data can be plotted as a line, or it can not. It can not be both. They are mutually exclusive definitions.(18 votes)

- i really wonder why math chose y and x(9 votes)
- Because y and x are fairly uncommon letters, I think.(8 votes)

- where is this used in real life?(8 votes)
- Marketing,stock prices,net income,etc(2 votes)

- If anyone is still watching this, why does he say "in respect too"??(4 votes)
- It's just a way of speaking. You know, some people like to talk differently, for example, ppl who say 'like' a lot or something.(5 votes)

- do you have to graph to figure out if the equation is linear or nonlinear?(4 votes)
- That is a great question. The answer is no. This is how you figure it out. Let a = any number. If you can simplify the equation to

y = ax, it is a linear equation.(3 votes)

- what does it mean when there is a curved line on the graph(4 votes)
- what is the difference between a non linear fuction and a linear function(3 votes)
- A linear function has a constant rate of change while a non-linear function does not.(3 votes)

- Does the triangle stand for "change"? Or so called "delta"?(3 votes)
- Yes you are correct that in this type of mathematical context, triangle or delta stands for change (so delta y means change in y, and delta x means change in x).

Have a blessed, wonderful day!(2 votes)

- I don't understand what the triangle that Sal puts next to x and y means. Can someone help me? I have a quiz about this tomorrow and I'm very confused.(3 votes)
- The triangle is the Greek letter "Delta" which is just short for "Change in".(2 votes)

- Can your rate of change be represented as Δx/Δy instead of Δy/Δx ?(3 votes)
- Not really, because I would suppose that everyone in the professional and amateur world of mathematics use Δy/ Δx instead of Δx/ Δy, and Δx/ Δy would confuse them, or they would assume you are wrong.(0 votes)

## Video transcript

Does the following table
represent a linear equation? So let's see what's
going on here. When x is negative 7, y is 4. Then when x is
negative 3, y is 3. So let's see what happened
to what our change in x was. So our change in
x-- and I could even write it over here,
our change in x. So going from negative
7 to negative 3, we had an increase in 4 in x. And what was our change in y? And this triangle, that's
just the Greek letter delta. It's shorthand for "change in." Well, our change in y
when x increased by 4, our y-value went from 4 to 3. So our change in
y is negative 1. Now, in order for this
to be a linear equation, the ratio between our change
in y and our change in x has to be constant. So our change in
y over change in x for any two points
in this equation or any two points in the table
has to be the same constant. When x changed by 4, y
changed by negative 1. Or when y changed by
negative 1, x changed by 4. So we have to have a
constant change in y with respect to x
of negative 1/4. Let's see if this is true. So the next two points, when
I go from negative 3 to 1, once again I'm
increasing x by 4. And once again, I'm
decreasing y by negative 1. So we have that same ratio. Now, let's look at
this last point. When we go from 1 to
7 in the x-direction, we are increasing by 6. And when we go from 2 to 1,
we are still decreasing by 1. So now this ratio, going
from this third point to this fourth point,
is negative 1/6. So it is not. So just for this last
point right over here, for this last point, our change
in y over change in x, or I should say, really, between
these last two points right over here, our change
in y over change in x-- let me clear this up. Let me make it clear. So just between these
last-- in magenta. Just between these last
two points over here, our change in y is negative
1, and our change in x is 6. So we have a different rate of
change of y with respect to x. Because we had a different
rate of change of y with respect to x, or ratio
between our change in y and change in x, this is
not a linear equation. No, not a linear equation.