Question

How do you decide whether these are linear or not linear?

Answer 1

if a line is straight then it's linear

Answer 2

A linear equation is of the form Ax + By = C, with at least of one of A and B \(\neq 0\). In other words, it must have a variable term without a power (a first degree term).

If you are looking at a graph, like @alexwee123 said, if the graph is a straight line, then it's a linear function. If not (if it curves or changes direction, etc) then it is non-linear.

Answer 3

How to tell whether this is linear or not?

Answer 4

@DebbieG

Answer 5

OK, #'s 3 - 6?

You are correct on 3 & 4.

On #5, you have to simplify to see whether it's linear or not. You distribute the 2x through the parentheses, and you get \(\large f(x)=6x-x^2\). That \(x^2\) means that it is NOT linear (it's a quadratic).

Answer 6

And you are correct that #6 is not linear - again, you have a 2nd degree term, so not linear.

But, your evaluations of the functions in 5 & 6 for the given values of x were incorrect - do you understand now what your errors were there?

Answer 7

Oh they are not my errors this is my friend's paper and i"m studying for the quiz with it. Sorry for the confusion. I know how he got 35 and 5 for #3. But i don't get how he got that it is a linear line. Can you explain that for me please?

Answer 8

OK - he has the function f(x)=5x - 10

That is just function notation for y=5x - 10

Now, that's is y = mx + b form for the equation for a line, so you can just see that it's a line, therefore it's linear.

To put it in terms of the definition that I gave above:

y=5x - 10
-5x + y = -10
5x - y = 10

So that is "standard form", Ax + By = C, with A=5, B=1 and C=10

Answer 9

Oh okay thanks you so much <3