How do you graph the inequality 3x-y<=6 ?

May 26, 2017

See the explanation.

Explanation:

Graph:

$3 x - y \ge 6$

Change the equation to the slope intercept form by solving for $y$.

Subtract $3 x$ from both sides.

$\textcolor{red}{\cancel{\textcolor{b l a c k}{3 x}}} - \textcolor{red}{\cancel{\textcolor{b l a c k}{3 x}}} - y \ge 6 - 3 x$

Simplify.

$- y \ge - 3 x + 6$

Multiply both sides by $- 1$. This will change the direction of the inequality.

$y \le 3 x - 6$

Determine some points on the line by picking values for $x$ and solving for $y$.

Points
$x = - 2 ,$$y = - 12$
$x = 0 ,$$y = - 6$
$x = 2 ,$$y = 0$

Plot the points, and draw a straight solid line through them. Then shade the area below the line.

Graph graph{y<=3x-6 [-15.7, 16.32, -13.07, 2.95]}