Question

1. which graph represents the following inequality. (1 point)

$6y + 15 \leq 12x + 27$
a. graph a
b. graph b
c. graph c
d. graph d

Explanation:

Step1: Simplify the inequality

Subtract 15 from both sides:
$6y \leq 12x + 12$

Step2: Isolate y variable

Divide all terms by 6:
$y \leq 2x + 2$

Step3: Identify line type

Since the inequality is $\leq$, the boundary line is solid (not dashed).

Step4: Test a point for shading

Use $(0,0)$: $0 \leq 2(0)+2$ → $0 \leq 2$, which is true. So shade the region containing $(0,0)$.

Answer:

B. <The graph with a solid line $y=2x+2$ and shading below/left of the line, containing the origin>