Question

The function rule that relate the given function's input and output is .

• A. $y=-\frac{2}{3}x$
• B. $y=-\frac{3}{2}x$
• C. $y=-4x$
• D. $y=\frac{3}{2}x$

Answer 1

The correct option is B $y=-\frac{3}{2}x$

From the system, we can see that:
$\text{When input (x) is 8, then output (y) is -12.}$

Let's analyze the options given.

$\text{Consider the equation y = -4}x.$
Substituting x = 8 in the above, we get:
$y=-4\times 8=-32$
This is not the correct output from the system.
$\text{∴ y = -4x is not the correct function rule.}$


$\text{Consider the equation y =}$ $\frac{3}{2}x.$
Substituting x = 8 in the above, we get:
$y=\frac{3}{2}\times 8=12$
This is not the correct output from the system.
$\text{∴ y =}$ $\frac{3}{2}x$$\text{is not the correct function rule.}$


$\text{Consider the equation y =}$ $-\frac{3}{2}x.$
Substituting x = 8 in the above, we get:
$y=-\frac{3}{2}\times 8=-12$
This is the correct output from the system.
$\text{∴ y =}$ $-\frac{3}{2}x$$\text{is the correct function rule.}$


$\text{Consider the equation y =}$ $-\frac{2}{3}x.$
Substituting x = 8 in the above, we get:
$y=-\frac{2}{3}\times 8=-\frac{16}{3}$
This is the correct output from the system.
$\text{∴ y =}$ $-\frac{2}{3}x$$\text{is not the correct function rule.}$

$\text{So, y =}$ $-\frac{3}{2}x$$\text{is the correct function rule for the image.}$