Question

1. which equation represents a linear function?

a. $y = 5x^2$
b. $y = \frac{3}{x} + 6$
c. $y = 2x + 4$
d. $y = x^3$

Explanation:

Step1: Recall linear function form

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

Step2: Analyze Option A

$y=5x^2$ has $x$ raised to the 2nd power, so it is quadratic, not linear.

Step3: Analyze Option B

$y=\frac{3}{x}+6$ can be rewritten as $y=3x^{-1}+6$, with $x$ raised to the -1st power, so it is not linear.

Step4: Analyze Option C

$y=2x+4$ matches the form $y=mx+b$ (where $m=2$, $b=4$), with $x$ to the 1st power, so it is linear.

Step5: Analyze Option D

$y=x^3$ has $x$ raised to the 3rd power, so it is cubic, not linear.

Answer:

C. $y = 2x + 4$