QUESTION IMAGE
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 )
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.
Snap & solve any problem in the app
Get step-by-step solutions on Sovi AI
Photo-based solutions with guided steps
Explore more problems and detailed explanations
B. $y=-\frac{3}{4}x - 5$