Answer:
Option 3
Step-by-step explanation:
Given : Inequality [tex]2x-3y<12[/tex]
To find : Which is the graph of linear inequality ?
Solution :
Inequality [tex]2x-3y<12[/tex]
Solve for y,
[tex]2x-12 < 3y[/tex]
[tex]y>\frac{2}{3} x-4[/tex]
Now, We plot the graph of the equation using x-intercept and y-intercept,
x-intercept is when y=0,
[tex]\frac{2}{3} x-4=0[/tex]
[tex]\frac{2}{3} x=4[/tex]
[tex]x=6[/tex]
y-intercept is when x=0,
[tex]\frac{2}{3}(0)-4=y[/tex]
[tex]y=-4[/tex]
So, Graph passing through (0,-4) and (6,0).
Now, The area of the graph is
Put x=0 and y=0
[tex]2(0)-3(0)<12[/tex]
[tex]0<12[/tex]
It is true. So, The region is towards origin.
The inequality is not have equal sign so the line is dotted.
From the given graph Option 3 is correct.
Refer the attached figure below.
