Question

which of the relationships below represents a function with the same rate of change as the function $y=\frac{5}{2}x - 2$?
a

$x$	$y$
6	34
8	46
10	58

b

$x$	$y$
8	9
12	12
16	15

c
coordinate plane with a line graph
d
coordinate plane with a line graph

Explanation:

Step1: Identify target rate of change

The given function is $y=\frac{5}{2}x - 2$, which is in slope-intercept form $y=mx+b$. The rate of change (slope) $m=\frac{5}{2}=2.5$.

Step2: Calculate slope for Option A

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take $(4,22)$ and $(6,34)$:
$m=\frac{34-22}{6-4}=\frac{12}{2}=6$

Step3: Calculate slope for Option B

Take $(4,6)$ and $(8,9)$:
$m=\frac{9-6}{8-4}=\frac{3}{4}=0.75$

Step4: Calculate slope for Option C

Take points $(0,-4)$ and $(2,1)$ from the graph:
$m=\frac{1-(-4)}{2-0}=\frac{5}{2}=2.5$

Step5: Calculate slope for Option D

Take points $(0,1)$ and $(2,-1)$ from the graph:
$m=\frac{-1-1}{2-0}=\frac{-2}{2}=-1$

Answer:

C