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## 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

CCSS.Math:

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(5 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.(13 votes)

- i really wonder why math chose y and x(4 votes)
- Because y and x are fairly uncommon letters, I think.(6 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)

- where is this used in real life?(6 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"?(2 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)

- 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)

- How do you find rules of tables with "x" decreasing by 3 and"y" increases by 1(2 votes)
- Consider the following: {(10,6), (7,7), (4,8),(1,9)}.

That's the best I could do for generating a Table here.

There is a postulate (a rule) from geometry that says any two points determine a line.

1. Pick two points from the above set, for example (7,7) and (1,9).

2. Calculate the slope of the line between them: m = (9 - 7)/(1 -7)= - 2/6 = -1/3.

3. Use one of the points (It doesn't matter which point you choose, either one will work. But you have to be consistent, you can't mix the coordinates. If you use the x-coordinate of a particular point then you have to use the y-coordinate of that same point.) as a reference point to write the equation of the line in point-slope form: y - 7 = -1/3(x -7).

4. Technically, you're done because this is the equation of the line in point-slope form. However, if you want it in slope-intercept form then you need to substitute the point (0,b) into the point-slope form that you just figured out: b - 7 = -1/3(0-7).

5. From step (4) you get b = 7/3 + 7 =28/3.

6. Now, you can write the equation as y = -1/3 x + 28/3.

If you want to check it, you can pick any other point from the Table, substitute its coordinates into the equation, and you should generate a true statement: 6 = -1/3(10) + 28/3 = 18/3 =6.(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.