To know which graph is it, we have to calculate the straight-line equation, preferably with the form:
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
As we have the inequality:
[tex]3y-9\le6x[/tex]
We have to isolate y:
0. Adding 9 to both sides of the equation.
[tex]3y-9+9\le6x+9[/tex][tex]3y\le6x+9[/tex]
2. Dividing both sides of the equation against 3:
[tex]\frac{3y}{3}\le\frac{6x+9}{3}[/tex][tex]y\le2x+3[/tex]
Then, we have the y-intercept which is (0, 3). Additionally, with the inequality sign, we can see that it includes all the y values below or equal that equation, meaning that a continuous line will be placed (instead of a discontinuous).
Answer: A.
