9x+3y-6<_ 0 I need help breaking this down

Question

asked Aug 24, 2024 84.4k views

1 Answer

Anton Holmberg · Answer 1 · 2024-08-29T01:16:16+0000

Answer:

$y \le -3x + 2$

Explanation:

We can rewrite the inequality:

$9x + 3y - 6 \le 0$

in slope-intercept form by isolating y.

First, we can add 6 to both sides.

$9x + 3y - 6 + 6 \le 0 + 6$

$9x + 3y \le 6$

Next, we can subtract
from both sides.

$9x + 3y - 9x \le 6 - 9x$

$3y \le 6 - 9x$

Then, we can divide both sides by 3.

$(3y)/(3) \le (6 - 9x)/(3)$

$y \le 2 - 3x$

Finally, we can re-arrange the right side to fit the slope-intercept form model:

y = mx + b

where
is the boundary line's slope and
is its y-intercept.

$\boxed{y \le -3x + 2}$