Question

y≤x−2

y ≥ \\(\frac{1}{4}\\)x − 4

(graph with two lines and regions a, b, c, d)

a. region c
b. region a
c. region b
d. region d

Explanation:

Step1: Analyze \( y \leq x - 2 \)

The line \( y = x - 2 \) has a slope of 1 and y - intercept - 2. The inequality \( y \leq x - 2 \) means the region below (or on) this line.

Step2: Analyze \( y \geq \frac{1}{4}x - 4 \)

The line \( y=\frac{1}{4}x - 4 \) has a slope of \( \frac{1}{4} \) and y - intercept - 4. The inequality \( y\geq\frac{1}{4}x - 4 \) means the region above (or on) this line.

Step3: Find the intersection region

We need to find the region that is below \( y = x - 2 \) and above \( y=\frac{1}{4}x - 4 \). By looking at the graph, Region B is below \( y=x - 2 \) (since for points in B, their y - values are less than or equal to the y - values on \( y = x - 2 \)) and above \( y=\frac{1}{4}x - 4 \) (since for points in B, their y - values are greater than or equal to the y - values on \( y=\frac{1}{4}x - 4 \)).

Answer:

C. Region B