Question

graphing an inequality
graph the solution set for this inequality
$-6x - 3y \leq -18$

step 1: identify the $x$- and $y$-intercepts of the boundary line.
when $x = 0, y = $
when $y = 0, x = $

options for intercepts: -3, -6, 6

Explanation:

Step1: Find y-intercept (x=0)

Substitute $x=0$ into $-6x-3y=-18$:
$$-6(0) - 3y = -18$$
$$-3y = -18$$
$$y = \frac{-18}{-3} = 6$$

Step2: Find x-intercept (y=0)

Substitute $y=0$ into $-6x-3y=-18$:
$$-6x - 3(0) = -18$$
$$-6x = -18$$
$$x = \frac{-18}{-6} = 3$$

Answer:

When $x=0$, $y=6$
When $y=0$, $x=3$

Table of intercepts:

$x$	$y$
3	0