Question

Which of the following represents a linear, but not proportional relationship?

• A. $x=\frac{y+5}{4}$
• B. Both $\left(A\right)\text{and}\left(B\right)$
• C.
• D. Neither $\left(A\right)\text{nor}\left(B\right)$

Answer 1

The correct option is A $x=\frac{y+5}{4}$

Given,
$x=\frac{y+5}{4}$
$\Rightarrow 4x=y+5$
$\Rightarrow 4x-5$

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.
$y=4x-5$ is of the form $y=mx+b$, where $m=4$ and $b=-5$.
So, $y=4x-5$ represents a linear function.

We also know that only linear functions of the form $y=mx$ are proportional.
Hence, the given function is linear, but not proportional.

Option B
We know that all the linear functions can be written in the form of $y=mx+b$, which graphically represents a straight line.
Hence, the graph of a linear function is a straight line.

The given graph does not represent a straight line.
Hence, the given graph does not represent a linear function.

Option A is correct.