Question

Which of the following represents linear and proportional relationships?

Answer 1

We know that all the functions of the form $y=mx+b$ are linear, where $m$ is the slope and $b$ is the $y-$intercept.

$y=10x+5$ is of the form $y=mx+b$, where $m=10$ and $b=5$.
So, $y=10x+5$ represents a linear function.

$y=10x-5$ is of the form $y=mx+b$, where $m=10$ and $b=-5$.
So, $y=10x-5$ represents a linear function.

We also know that only linear functions of the form $y=mx$ are proportional.

Hence, the given functions $y=10x+5$ and $y=10x-5$ are linear, but not proportional.

Option D is correct.