Does "y (2 + x) = 3" represents a straight line equation? [closed]

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.

• Dividing both sides by $2+x$ yields $y=\frac{3}{2+x}$, which is nonlinear considering it is a reciprocal function.
– JC12
Jul 13, 2020 at 4:41
• 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. Jul 13, 2020 at 4:41

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.
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.