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Question

# Is every linear equation is linear function ?

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Solution

## 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: $\mathrm{x}=-3\phantom{\rule{0ex}{0ex}}2\mathrm{x}+3\mathrm{y}=7\phantom{\rule{0ex}{0ex}}\mathrm{x}–5\mathrm{y}+8=0$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.

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