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I'm new to straight line equation and trying to find out whether $y (2 + x) = 3$ represents a straight line equation or not. Could anybody please help me to figure out how to reach a conclusion here.

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    $\begingroup$ Dividing both sides by $2+x$ yields $y=\frac{3}{2+x}$, which is nonlinear considering it is a reciprocal function. $\endgroup$
    – JC12
    Jul 13, 2020 at 4:41
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    $\begingroup$ Try picking some values of $x$ and see the corresponding vertical coordinate $y$ is. For example, $x=0$ means $2y=3$, so $y=3/2$. Do this a couple more times, and you will see that this equation does not describe a line. $\endgroup$
    – pancini
    Jul 13, 2020 at 4:41

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No it does not, It represents a hyperbola.
General equation of a straight line is $ax+by+c=$ where $a,b,c \in\mathbb R$. But your equation when simplified looks like $2y+xy-3=0$ Notice that straight line equation has no $xy$( or coefficient term $xy$ term is zero) hence it does not represent a straight line.

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There's a simple way to distinguish between a linear equation (or any polynomial) and a non-polynomial equation. A polynomial is defines as $$y=a_1x^1 + a_2x^2 + ... + a_nx^n$$ Observe the variable $x$ is on one side and $y$ is on the other, this is the general form. So bring one of the variable to one side and see if the degree is a positive integer, only then the equation is a polynomial.
Try using this information for your question. (A linear equation is an equation of degree 1)

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