Is the following equation linear? Given the equation:
$$-\dfrac{3}{x} + y = 10$$
Is this equation linear? Yes or no? Please explain.
I have tried 7 other problems like this and easily figured it out, since this is written differently (a negative fraction and the $y$ isn't by itself).
I don't know what to do.
 A: Upon rearrangement, we find
$$-3 + xy - 10x = 0$$
This is not linear, since linear equations can always be put in the form
$$ax + by + c = 0$$
The $xy$ means we can't.
A: For Lienar equations in two or more than two variables,
In order to be a linear equation, the powers of $x_1, \dots , x_n$ must be equal to $1$, not be bigger than $1$. 
The general linear equation in n variable is the following form; 
$$ a_1x_1+\cdots + a_nx_n=c$$ $a_i$'s any number. And $c$ is constant. 
As for your equation,
$$-10x+xy=3$$
This equation consists of two variables $x$ any $y$ 
The powers of $x$ are all $1$. And the power of $y$ is $1$. 
All is okay so far. However,
since $\exists$ $xy$ in the equation,  the equation is not linear. 
A: If the equation were linear, then its graph (in the $xy$-plane) would be a straight line. However, check that the following points indeed lie on the graph:
$(1,13)$
$(-1,7)$
$(-\frac{3}{10},0)$
Can there be a straight line passing through these three points?
I hope this helps! (Of course, there's a formal proof that the equation isn't linear given in the nice answer by T. Bongers above. However, when you see an equation and you think it's linear (or not), then you should note that the graph must be a straight line. That's the intuition behind linear equations. It's worth plotting the entire graph to see what it looks like but just plotting the three points above should show you that the equation is not linear.)
Edit:
The following image is provided by User:ali (https://math.stackexchange.com/users/78741/ali). I think it's a fantastic addition to my answer and credit should go to him for it (thanks!). (You can clearly see here that the equation isn't linear. Exercise: Can you confirm visually that the three points above lie on this graph?)

A: Here is the general form for a linear equation, so you can compare

$$y := m x + b\quad m,b\in \mathbb{R}. $$ 

