Question

which equation is a linear function?
$y = \frac{2}{x}+3$
$y = 2^{x}-1$
$y = x^{2}+7$
$y = \frac{x}{2}-5$

Explanation:

Step1: Recall linear - function form

A linear function has the form $y = mx + b$ where $m$ and $b$ are constants and the highest power of the variable $x$ is 1.

Step2: Analyze $y=\frac{2}{x}+3$

This is a rational function since it has $x$ in the denominator, not linear.

Step3: Analyze $y = 2^{x}-1$

This is an exponential function as the variable $x$ is in the exponent, not linear.

Step4: Analyze $y=x^{2}+7$

This is a quadratic function as the highest - power of $x$ is 2, not linear.

Step5: Analyze $y=\frac{x}{2}-5$

This can be written as $y=\frac{1}{2}x - 5$, which is in the form $y = mx + b$ with $m=\frac{1}{2}$ and $b=-5$, so it is a linear function.

Answer:

$y=\frac{x}{2}-5$