Question

which equation represents a linear function?
$y = x - 3$
$y = x^2 - 3$
$y = x^3 - 3$
$y = \sqrt{x} - 3$

Explanation:

Step1: Recall linear function definition

A linear function has the form $y=mx+b$, where the highest power of $x$ is 1, no roots/powers >1.

Step2: Analyze each option

• $y=x-3$: Power of $x$ is 1, matches form.
• $y=x^2-3$: Power of $x$ is 2, not linear.
• $y=x^3-3$: Power of $x$ is 3, not linear.
• $y=\sqrt{x}-3$: Equivalent to $y=x^\frac{1}{2}-3$, power not 1, not linear.

Answer:

$y=x-3$