- 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
Linear & nonlinear functions: table
Learn to determine if a table of values represents a linear function. Created by Sal Khan.
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- what if the table can be both linear and nonlinear?. thank you(6 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.(15 votes)
- i really wonder why math chose y and x(6 votes)
- Because y and x are fairly uncommon letters, I think.(8 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"?(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)
- 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)
- the graph of y= (2+x)(4-x) has a turning point at M and cuts the x-axis at P and Q and the y-axis at R.Find the coordinates of P and Q.(2 votes)
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.