Question

question\
which of the relationships below represents a function with the same rate of change as the function $y = -4x + 3$?\
a\

$x$	$-2$	$2$	$6$	$10$	\
$y$	$3$	$-7$	$-17$	$-27$	\

b\
(there is an image of a graph here)\
c\
(there is an image of a graph here)\
d\

$x$	$-4$	$0$	$4$	$8$	\
$y$	$-7$	$5$	$17$	$29$

Explanation:

Step1: Identify target rate of change

The given function $y = -4x + 3$ is in slope-intercept form $y=mx+b$, where $m$ is the rate of change (slope). So the target slope is $m=-4$.

Step2: Calculate slope for Option A

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take points $(-2,3)$ and $(2,-7)$:
$m=\frac{-7-3}{2-(-2)}=\frac{-10}{4}=-2.5$

Step3: Calculate slope for Option B

Take two points on the line, e.g., $(0,-1)$ and $(-1,3)$:
$m=\frac{3-(-1)}{-1-0}=\frac{4}{-1}=-4$

Step4: Calculate slope for Option C

Take two points on the line, e.g., $(0,6)$ and $(-3,0)$:
$m=\frac{0-6}{-3-0}=\frac{-6}{-3}=2$

Step5: Calculate slope for Option D

Use slope formula with points $(-4,-7)$ and $(0,5)$:
$m=\frac{5-(-7)}{0-(-4)}=\frac{12}{4}=3$

Answer:

B. The linear graph with a slope of -4