In the rectangular coordinate system shown above, does the

[RonPurewal]

You're welcome.

[angierch]

Hi, I have a doubt concerning statement 2 of this problem. I am not sure the reason that statement 2 is insufficient.

Here is my reasoning:

statement 2) Statement to translates to b=-6 or one of line k's points is (0,-6). Therefore, line k could be:

x=0, which makes the statement false.

or

any other line that has a positive or negative slope, which makes the statement true.

Therefore, statement 2 is insufficient.

Now, one question can I infer from statement 2 that the line k can be x=0 (b in x=0 has many different values) ?

second question, is my reasoning above correct?

Thank you,
Angelica R.

[RonPurewal]

This is not accurate:

any other line that has a positive or negative slope, which makes the statement true.

Nope.
Through the given point (0, -6), lines with negative slopes will hit quadrant II. Lines with positive slopes will not hit it.
That's already proof that the statement is not sufficient.

In general, you won't need "tricky" cases to solve the problems. Even if you think of them, as you did here, they won't change the outcome.

(Quadrant II is the quadrant on the top left; perhaps that's the misunderstanding. If quadrant II were one of the bottom quadrants, then what you wrote in my quote above would be true.)

[angierch]

Understood. Thank you much! This was helpful.

[RonPurewal]

You're welcome.