Question

1. graph the linear inequality below.

y < -5x - 4

1. graph the linear inequality below.

12x + 6y ≤ 18

Explanation:

Step1: Rewrite inequality to slope-intercept form

Start with $12x + 6y \leq 18$. Isolate $y$:

$$\begin{align*} 6y &\leq -12x + 18\\ y &\leq -2x + 3 \end{align*}$$

Step2: Identify slope (m) and intercept (b)

From $y \leq -2x + 3$, compare to $y=mx+b$:
$m = -2$, $b = 3$

Step3: Determine line type and shading

Inequality uses $\leq$, so use a solid line. Shade below the line (since $y$ is less than or equal to the expression).

Step4: Plot key points for the line

• y-intercept: $(0, 3)$
• x-intercept (set $y=0$): $0 = -2x + 3 \implies x = 1.5$, so $(1.5, 0)$

Answer:

Slope $m=-2$, y-intercept $b=3$. To graph:

1. Draw a solid line through $(0, 3)$ and $(1.5, 0)$.
2. Shade the region below this solid line.