The graph above shows line \(H.\) Line \(J\) (not shown) does not pass through the first quadrant. Which of the followin

M7MBA wrote: ↑

Sun Jun 14, 2020 1:49 pm

line H graph.JPG

The graph above shows line \(H.\) Line \(J\) (not shown) does not pass through the first quadrant. Which of the following could be true?

I. line \(J\) is perpendicular to line \(H.\)
II. line \(J\) is parallel to line \(H.\)
III. line \(J\) intersect line \(H\) in the third quadrant

(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III

[spoiler]OA=D[/spoiler]

Solution:

Let’s analyze each statement.

I. Line J is perpendicular to line H.

This is possible since a line perpendicular to line H can only pass through Q II and Q IV if its y-intercept is 0, or it can only pass through Q II, Q III, and Q IV if its y-intercept is negative. In either case, we see that it doesn’t need to pass through Q I.

II. Line J is parallel to line H.

This is not possible since any line parallel to lin H will also have the same slope, which is a positive slope. Any positive-sloped line must pass through Q I.

III. Line J intersects line H at the third quadrant.

This is possible since, for example, if line J is a vertical line such that it intersects line H at the third quadrant, then it only passes through Q II and Q III, without passing through Q I.

Answer: D