Graph the inequality. $- x + 3 y

Question

Graph the inequality. $- x + 3 y < - 9$

Quizplus · Accepted Answer

To graph the inequality, we first need to rewrite it in slope-intercept form:
$$y > \frac13 x - 3$$
Next, we will graph the line with slope $\frac13$ and $y$-intercept $-3$ (dashed line):
[asy]
size(160);
import TrigMacros;
rr_cartesian_axes(-8,8,-8,8);
real f(real x) {return (1/3)*x-3;}
draw(reflect((0,0),(1,1))*(graph(f,-8,8)),linetype("8 8"));
label("$y=\frac{1}{3}x-3$",(8,-7),NE);
[/asy]
Since the inequality is strictly less than $-9$, we shade the region below the line:
[asy]
size(160);
import TrigMacros;
rr_cartesian_axes(-8,8,-8,8);
real f(real x) {return (1/3)*x-3;}
fill(((-8,-8)--(-8,0)--(8,0)--(8,-8)--cycle),gray(0.7));
draw(reflect((0,0),(1,1))*(graph(f,-8,8)),linetype("8 8"));
label("$y=\frac{1}{3}x-3$",(8,-7),NE);
draw((-8,-9)--(8,-9),Arrows);
draw((0,-6)--(0,6),Arrows);
label("$y$", (0,6), N);
label("$x$", (8,0), E);
[/asy] 
Note that since the inequality is strict ($<$), the boundary line is not part of the solution. Thus, we use a dashed line to graph the boundary line. The shaded area represents the region satisfying the inequality. Therefore, the correct choice is (B).

Graph the Inequality −x+3y<−9- x + 3 y < - 9−x+3y<−9

Graph the Inequality $- x + 3 y < - 9$