Question

graph the inequality on the axes below.
$x - 6y > 18$

Explanation:

Step1: Rewrite to slope-intercept form

Isolate $y$ to simplify graphing.

$$\begin{align*} x - 6y &> 18 \\ -6y &> -x + 18 \\ y &< \frac{1}{6}x - 3 \end{align*}$$

Note: Inequality flips when dividing by a negative number.

Step2: Identify boundary line

The boundary uses the equality $y = \frac{1}{6}x - 3$. Since the inequality is $<$ (not $\leq$), the line is dashed.

• y-intercept: $(0, -3)$
• Slope: $\frac{1}{6}$ (rise 1, run 6)

Step3: Determine shaded region

Test the origin $(0,0)$ in the inequality:
$$0 < \frac{1}{6}(0) - 3 \implies 0 < -3$$
This is false, so shade the region below the dashed boundary line.

Answer:

1. Draw a dashed line with y-intercept $(0, -3)$ and slope $\frac{1}{6}$ (e.g., plot a second point at $(6, -2)$ and connect to $(0, -3)$ with a dashed line).
2. Shade the entire area below this dashed line.