Question

the table below represents a linear function.

x	y
-4	11
-2	6
0	1

which relationship represents a function with a greater slope than the function represented above?

a (image of a line graph)

b ( y = -\frac{3}{4}x - 5 )

c (image of a line graph)

d ( y = -\frac{5}{2}x - 4 )

Explanation:

Step1: Calculate slope of given table

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$. Take points $(-6,16)$ and $(-4,11)$:
$m=\frac{11-16}{-4-(-6)}=\frac{-5}{2}=-\frac{5}{2}$

Step2: Find slope of Option A

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

Step3: Identify slope of Option B

From $y=-\frac{3}{4}x-5$, slope $m=-\frac{3}{4}$

Step4: Find slope of Option C

Take points $(0,-3)$ and $(-2,2)$:
$m=\frac{2-(-3)}{-2-0}=\frac{5}{-2}=-\frac{5}{2}$

Step5: Identify slope of Option D

From $y=-\frac{5}{2}x-4$, slope $m=-\frac{5}{2}$

Step6: Compare slopes

We need a slope greater than $-\frac{5}{2}$. Since $-\frac{3}{4} > -\frac{5}{2}$, Option B has a greater slope.

Answer:

B. $y=-\frac{3}{4}x - 5$