Question

Which of the following represents a linear function?

• A.
• B. All of the above
• C. $y=6x+5$
• D.

  $x$	$1$	$3$	$5$	$7$
  $y$	$1$	$13$	$25$	$37$

Answer 1

The correct option is B All of the above

Option A

$x$	$1$	$3$	$5$	$7$
$y$	$1$	$13$	$25$	$37$

The slope between the first and the second points $=\frac{(13-1)}{(3-1)}=\frac{12}{2}=6$

The slope between the second and the third points $=\frac{(25-13)}{(5-3)}=\frac{12}{2}=6$

The slope between the third and the fourth points $=\frac{(37-25)}{(7-5)}=\frac{12}{2}=6$

Since the slope is constant, the given function is linear.

Option B

$y=6x+5$

We know that all the functions of the form $y=mx+b$ are linear.

$y=6x+5$ is of the form $y=mx+b$, where $m=6$ and $b=5$.
So, $y=6x+5$ represents a linear function.

Option CWe 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 represents a straight line.
Hence, the given graph represents a linear function.
Hence, all the three options represent a linear function.

Option D is correct.