1. **State the problem:** We need to determine if the points $(0, -27)$ and $(-9, 0)$ lie on the line given by the equation $$3y - 9x = 18.$$\n\n2. **Rewrite the equation in slope-intercept form:**\nStart with the original equation:\n$$3y - 9x = 18.$$\nAdd $9x$ to both sides:\n$$3y = 9x + 18.$$\nDivide both sides by 3:\n$$\cancel{3}y = \frac{9x}{\cancel{3}} + \frac{18}{\cancel{3}}$$\n$$y = 3x + 6.$$\nThis is the slope-intercept form $y = mx + b$ where $m=3$ and $b=6$.\n\n3. **Check if the point $(0, -27)$ lies on the line:**\nSubstitute $x=0$ and $y=-27$ into the equation $y = 3x + 6$:\n$$-27 \stackrel{?}{=} 3(0) + 6$$\n$$-27 \stackrel{?}{=} 0 + 6$$\n$$-27 \stackrel{?}{=} 6$$\nThis is false, so $(0, -27)$ is **not** on the line.\n\n4. **Check if the point $(-9, 0)$ lies on the line:**\nSubstitute $x=-9$ and $y=0$ into the equation $y = 3x + 6$:\n$$0 \stackrel{?}{=} 3(-9) + 6$$\n$$0 \stackrel{?}{=} -27 + 6$$\n$$0 \stackrel{?}{=} -21$$\nThis is false, so $(-9, 0)$ is **not** on the line.\n\n**Final answer:** Neither $(0, -27)$ nor $(-9, 0)$ lies on the line $3y - 9x = 18$.