Question

given the linear inequality graph, which statements are true?
a point (-4, 2) is a solution
b the graph represents $y>3x - 6$
c the graph represents $y\geq3x - 6$
d all points in the blue area are solutions
e points on the solid line are not solutions

Explanation:

Step1: Identify line equation

The line passes through $(2,0)$ and $(0,-6)$. Slope $m=\frac{0-(-6)}{2-0}=3$. Using $y=mx+b$, $b=-6$, so line is $y=3x-6$.

Step2: Analyze inequality type

The line is solid, so inequality uses $\geq$ or $\leq$. Blue area is above the line, so $y\geq 3x-6$.

Step3: Check Option A

Substitute $(-4,2)$ into $y\geq 3x-6$: $2\geq 3(-4)-6 \implies 2\geq -18$, which is true.

Step4: Check Option B

$y>3x-6$ uses a dashed line, but graph has solid line, so false.

Step5: Check Option C

$y\geq 3x-6$ matches solid line and shaded area, so true.

Step6: Check Option D

By definition, shaded area contains all solutions, so true.

Step7: Check Option E

Solid line means points on it are solutions, so false.

Answer:

A. Point (-4, 2) is a solution
C. The graph represents $y\geq 3x - 6$
D. All points in the blue area are solutions