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
graph of a line
b

x	y
4	5
6	10
8	15

c
graph of a line
d

x	y
8	-9
12	-14
16	-19

answer
○ a ○ b
○ c ○ d

Explanation:

Step1: Identify target slope

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

Step2: Calculate slope of Option A

Use two points on the line, e.g., $(-6,0)$ and $(0,3)$.
Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
$m = \frac{3 - 0}{0 - (-6)} = \frac{3}{6} = 0.5$

Step3: Calculate slope of Option B

Use two points from the table, e.g., $(2,0)$ and $(4,5)$.
$m = \frac{5 - 0}{4 - 2} = \frac{5}{2} = 2.5$

Step4: Calculate slope of Option C

Use two points on the line, e.g., $(0,5)$ and $(2,0)$.
$m = \frac{0 - 5}{2 - 0} = \frac{-5}{2} = -2.5$

Step5: Calculate slope of Option D

Use two points from the table, e.g., $(4,-4)$ and $(8,-9)$.
$m = \frac{-9 - (-4)}{8 - 4} = \frac{-5}{4} = -1.25$

Answer:

C