Question

concepts and connections-plc ing linear inequalities \\((-5, 2)\\) \\((2, 2)\\) \\((5, 2)\\) no solution

Explanation:

Step1: Find line equation

The dashed line passes through $(0,-1)$ and $(1,0)$. Slope $m=\frac{0-(-1)}{1-0}=1$. Using $y=mx+b$, $b=-1$, so line is $y=x-1$.

Step2: Identify inequality sign

Shaded region is below the dashed line, so $y < x - 1$.

Step3: Test each point

Test $(-5,2)$:

Substitute $x=-5,y=2$: $2 < -5 -1 \implies 2 < -6$, false.

Test $(2,2)$:

Substitute $x=2,y=2$: $2 < 2 -1 \implies 2 < 1$, false.

Test $(5,2)$:

Substitute $x=5,y=2$: $2 < 5 -1 \implies 2 < 4$, true.

Answer:

(5, 2)