Question

Which of the following does NOT represent a linear relationship?

• A. $y=\frac{x}{5}$
• B.

  $x$	$-4$	$0$	$4$	$8$	$12$
  $y$	$12$	$2$	$-6$	$2$	$12$

• C. $x=\frac{9}{7}y+4$
• D. $y=4x+7$

Answer 1

Answer: (B)

$x$	$-4$	$0$	$4$	$8$	$12$
$y$	$12$	$2$	$-6$	$2$	$12$

Options A, C and D are equations of a straight line.

Hence, they follow the linear relationship.

Consider option B.

If the given data of x and y follows linear relationship then $\frac{y_2-y_1}{x_2-x_1}=$ Constant $=$ slope.

Now $\frac{y_2-y_1}{x_2-x_1}=\frac{2-12}{0-(-4)}=\frac{-5}{2}$ ...(i)

Similarly, $\frac{y_3-y_2}{x_3-x_2}=\frac{-6-2}{4-0}=-2$...(ii).

Since $i\left(\right)\ne \left(ii\right)$, hence $x$ and $y$ does not follow a linear relationship.