Question

y = |x| + 5 According to the book this is not a linear equation, because "a linear equation in two variables is an equation that can be written in the form Ax + By = C"

original equation-->y = |x| + 5
subtract |x| from both sides--> y - |x| = 5

Why is this incorrect? Thank you.

Answer 1

not 100% sure, but im pretty sure this is why...
your supposed to undo everything being done to x, so your supossed to subtract 5 from both sides. not x itself.

Answer 2

What you've written is not incorrect.

Answer 3

But, when you have the absolute value, you're most likely going to wind up with 2 different functions, one where whats inside of the absolute value is negative and one where it's positive. This is how the absolute value operator is defined.

Answer 4

What this means mathematically is that if you have for example\[f(x)=|x|\]
It's the same thing as two different functions in different intervals of x.
When x is greater or equal to 0, you get the function f(x)=x and when x is less than 0, you get the function f(x)=-x. Just try to picture that graphically, it's quite easy when you get the hang of it. :D

Answer 5

Thank you. I put this in Wolfram Alpha and it graphed and passed the ever-popular straight line test, so I thought of course it's a linear equation. So I suppose my rule for now is if there is an absolute value operator in the equation, the chances are it's not linear. Is that a fair assumption to make considering my current level?

Answer 6

@Noliec ^^^

Answer 7

I would say so! If the function is linear or not depends like I said before, what x values you're looking at the function. If you look at all x values, it's not going to be linear, of course. :)

Answer 8

Great thank you very much.