In the rectangular coordinate system, if line l is parallel to one of

I am uploading a graph for anyone who needs clarification on why the answer is (C).


Statement (1) tells us that (4, -5) is on the graph of the line, but looking at the image above, we cannot tell whether that point exists on the red line, in which case the answer to the question would be yes, or on the green line, which would make the answer to the question no. Since both lines conform to the given information about line l being parallel to one of the axes, we cannot say that statement (1) is sufficient on its own.

Statement (2) is even more open-ended, with an infinite number of vertical lines possible in the image above. Of course, one of these, the red line, would lead to a yes answer, but any other line would lead to a no answer. Hence, statement (2) is not sufficient on its own.

Taken together, there is no way the line can be parallel to the x-axis, as the blue line shows, since it would not contain the point (4, -5) from statement (1) and would not cross the x-axis, per statement (2). The only valid line, the one that conforms to both statements, is the red line, and the answer to the question is yes, but only if both statements are taken together: (C).

I hope that helps if anyone was confused. Good luck with your studies.

- Andrew

In the rectangular coordinate system, if line l is parallel to one of the axes, does line contain the point (4, 5) ?

(1) Line l contains the point (4, -5).
Insufficient.
Line l can be a vertical line that contains (4,-5) and (4,5) OR
Line l can be horizontal and contain (4,-5) only

(2) Line l crosses the x-axis.
Clearly insufficient.

C: Sufficient (must be a vertical line that contains both).

Combine both the options
that means line apsses though x and parallel to y axis
and cut x at 4
so it will definitely pass through all values of y
thus it passes through 4,5 and 4,-5

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