Question

16/22
which function is linear?
$y = 2x + 4$
$y = 2x^2 + 4$
$y = 2x(4 - 3x)$
$xy = 15$

Explanation:

Step1: Recall linear function definition

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

Step2: Analyze first option

$y=2x+4$ matches $y=mx+b$ with $m=2$, $b=4$. Highest $x$ power is 1.

Step3: Analyze second option

$y=2x^2+4$ has $x$ raised to the power of 2, so it is quadratic, not linear.

Step4: Analyze third option

Expand $y=2x(4-3x)$:
$y=8x-6x^2$. This has $x^2$ term, so it is quadratic, not linear.

Step5: Analyze fourth option

Rewrite $xy=15$ as $y=\frac{15}{x}$, which is a reciprocal function, not linear.

Answer:

A. $y = 2x + 4$