The difference between A and B, and C and D is the continuous/discontinuous line.
When the line is discontinuous, it means the values are NOT included. In this case, the sing < or > is used.
When the line is continuous, it means the values ARE included. In this case, the sing ≤ or ≥ is used.
Now, to determine which graphic is the one of our function, we can get the intersections with the y- and x-axis.
• Intersection with y-axis: ,x = 0
[tex]3x+y>4[/tex][tex]3\cdot0+y>4[/tex][tex]y>4[/tex]
The intersection in y-axis happens on y > 4.
Intersection with x-axis: y = 0
[tex]3x+0>4[/tex][tex]x>\frac{4}{3}[/tex]
The intersection in y-axis happens on x > 4/3.
Answer: C.
