Answer:
[tex]y\geq \frac{1}{3}x-1[/tex]
Step-by-step explanation:
The graph that belong to the question is attached.
Options are:
[tex]y\geq \frac{1}{3}x-1 \\y\leq \frac{1}{3}x-1 \\y<3x-1\\y>3x-1[/tex]
In the graph we observe that it's a solid line, so its equation must have symbols like [tex]\leq ; \geq[/tex]. That only left option 1 and option 2 as possible answer.
Now, we take a test point, the easiest is [tex](0;0)[/tex], that is, [tex]x=0;y=0[/tex]. If we replace this test point in one expression and results a false statement, then that is not the answer, if result a true statement, then that's the answer.
Second expression test: [tex]y\geq \frac{1}{3}x-1[/tex]
[tex]0\geq \frac{1}{3}0-1\\0\geq -1[/tex]
We see that this inequality gave a true result, because zero is more than -1.
Therefore, the answer is the second option.
