Question

Is every linear equation is linear function ?

Answer 1

We know, a linear function is a function whose graph is a straight line.

A linear function can be described by a linear equation and a linear equation is a degree-$1$ polynomial.

Example:-

The following are linear equations:

$$\begin{gathered} \mathrm{x}=-3 \\ 2\mathrm{x}+3\mathrm{y}=7 \\ \mathrm{x}–5\mathrm{y}+8=0 \end{gathered}$$

Meanwhile, the following are not linear equations:

$\mathrm{xy}+6=\mathrm{x}+\mathrm{y}$ is not a linear equation because the term $\mathrm{xy}$ has degree $2$.

$\mathrm{x}+2{\mathrm{y}}^2=8$ is not a linear equation because the term $2{\mathrm{y}}^2$ has degree $2$.

That means all linear equations produce straight lines when graphed, but not all linear equations produce linear functions.

In order to be a linear function, a graph must be both linear (a straight line) and a function.

Hence, No, every linear equation is not a linear function.