Question

the table below represents a linear function.

x	y
7	-37
10	-52
13	-67

which relationship represents a function with the same rate of change as the function represented above?

a

$y = 3x + 3$

b

(graph of a line with x - intercept at 3 and y - intercept at 3, slope negative)

c

$y = 4x + 3$

d

(graph of a line with negative y - intercept, steep negative slope)

Explanation:

Step1: Calculate slope of table function

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take $(x_1,y_1)=(4,-22)$ and $(x_2,y_2)=(7,-37)$:
$m=\frac{-37-(-22)}{7-4}=\frac{-15}{3}=-5$

Step2: Find slope of Option A

For $y=3x+3$, slope is $3$.

Step3: Find slope of Option B

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

Step4: Find slope of Option C

For $y=4x+3$, slope is $4$.

Step5: Find slope of Option D

Use two points on the line: $(0,-5)$ and $(-1,0)$.
$m=\frac{0-(-5)}{-1-0}=\frac{5}{-1}=-5$

Answer:

D (the graph with slope -5)