Given a line  defined by the equation  with a slope of , any line perpendicular to  would have a slope that is the negative reciprocal of , . Given our equation  , we know that  and that . 

The only answer choice with this slope is . 

Given a line  defined by the equation  with a slope of , any line perpendicular to  would have a slope that is the negative reciprocal of , . Given our equation  , we know that  and that . 

There are two answer choices with this slope,  and  . 

For any line  with an equation  and slope , a line that is perpendicular to  must have a slope of , or the negative reciprocal of . Given , we know that  and therefore know that . 

Only one equation above has a slope of : . 

For any line  with an equation  and slope , a line that is perpendicular to  must have a slope of , or the negative reciprocal of . Given the equation , we know that  and therefore know that .

For any line  with an equation  and slope , a line that is perpendicular to  must have a slope of , or the negative reciprocal of . Given the equation , we know that  and therefore know that . 

Given a slope of , we know that there are two solutions provided:  and . 

First, we need to rearrange the equation into slope-intercept form.  .

  Therefore, the slope of this line equals  Perpendicular lines have slope that are the opposite reciprocal, or 

Opposite rays begin at the same endpoint; their directions are opposite each other. Since  has endpoint , we are looking for the ray that has endpoint  and goes in the opposite direction - this ray is  .

A ray can be named with two letters, the first of which must be its endpoint and the second of which can be any other point on the ray.

 has endpoint . The only other marked point on the ray is , so the correct choice is .

A ray starts at a single point and then continues in a straight line infinitely in some direction. The given ray starts at the point  ,  which is in quadrant  , so we immediately know this must be included in the answer. The ray has a positive slope of  ,  which means the next point is  ,  followed by  ,  ,  ,  ,  and so on. By plotting these points we can visualize that the ray starts in quadrant  ,  crosses through quadrant  ,  and then continues infinitely into quadrant  ,  without ever crossing through any part of quadrant  .  The answer, therefore, is the following three quadrants:

An angle, by definition, is the union of two rays with the same endpoint. Their common endpoint is the vertex of the angle, which is always named by the middle letter of a three-letter angle name. Therefore, we are looking for two rays with endpoint . Since the first letter of the name of a ray is always its endpoint, we are looking for two rays with  as the first letter in their names. This makes  and  the correct choice.