Without plotting $y$ against $x$ how could you tell the below were linear equations $y = 100 - \frac{9}{x}$ and $y = 2x^2 -10x.$
Thanks in advance!
Without plotting $y$ against $x$ how could you tell the below were linear equations $y = 100 - \frac{9}{x}$ and $y = 2x^2 -10x.$
Thanks in advance!
Well, the first one certainly isn't a linear equation because you have $1/x$ term in it. Linear always means you only have $x$ appearing in the equation. So definitely, the second one is a linear equation.
Using the definition of linear equation. A linear equation in variables $x$ and $y$ is an equation of the form: $Ax+By=C,$ for fixed constants $A$, $B$ and $C$ (with A^2+B^2>0). Do any of the equations you listed have this form?
One quick way is that linear equations have a degree of one (or, technically, zero). So, the x variable can only be raised to the power of one, no higher or lower. No x^2 or x^3 anywhere in the equation.
The first one has a x in the denominator, that's basically multiplying by an x to the power of -1. The second one has an x to the power of 2.
It depends on how your homework wants you to prove it, though.