Question

which of the relationships below represents a function with the same slope as the function $y = -\frac{3}{2}x - 4$?

a

$x$	$y$
$-4$	$9$
$-2$	$6$
$0$	$3$

b

$x$	$y$
$4$	$2$
$8$	$5$
$12$	$8$

Explanation:

Step1: Identify target slope

The given function is in slope-intercept form $y=mx+b$, where $m$ is the slope. So the target slope is $m = -\frac{3}{2}$.

Step2: Calculate slope for Option A

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take points $(-6,12)$ and $(-4,9)$:
$\frac{9-12}{-4-(-6)}=\frac{-3}{2}=-\frac{3}{2}$

Step3: Calculate slope for Option B

Take points $(0,-1)$ and $(4,2)$:
$\frac{2-(-1)}{4-0}=\frac{3}{4}$

Answer:

A.

$x$	$y$
$-4$	$9$
$-2$	$6$
$0$	$3$