Question

Which linear inequality is represented by the graph?

y ≤ One-thirdx − 1
y ≥ One-thirdx − 1
y < 3x − 1
y > 3x − 1

Answer 1

its option B

Explanation:

Answer 2

`y\geq  (1)/(3)x-1`

Explanation:

The graph that belong to the question is attached.

Options are:

`y\geq  (1)/(3)x-1 \\y\leq (1)/(3)x-1 \\y<3x-1\\y>3x-1`

In the graph we observe that it's a solid line, so its equation must have symbols like
`\leq ; \geq`. That only left option 1 and option 2 as possible answer.

Now, we take a test point, the easiest is
`(0;0)`, that is,
`x=0;y=0`. 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:
`y\geq  (1)/(3)x-1`

`0\geq  (1)/(3)0-1\\0\geq -1`

We see that this inequality gave a true result, because zero is more than -1.

Therefore, the answer is the second option.