Is $\frac{1}{x} + 3 y = - 5$ $1/x+3y=-5$ a linear function and explain your reasoning?

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Answer 1 · 2017-01-16T23:09:22

This is not a linear function. Explanation below.

We can modify the expression, so it has $y$ $y$ alone on one side:

$3 y = - \frac{1}{x} - 5 \Rightarrow y = - \frac{1}{3} \frac{1}{x} - 15$ $3y = -1/x -5 => y = -1/3 1/x - 15$ .

We can see that this is basically the hyperbola $y = - \frac{1}{3} \frac{1}{x}$ $y = -1/3 1/x$

shifted 15 units downwards, and hyperbolas are not linear functions.

Is 1x+3y=−51/x+3y=-5 a linear function and explain your reasoning?