The equation for a line in standard form is written as follows:

Where  is the slope of the line and  is the y intercept. By definition, the slope of a line is the negative reciprocal of the slope of the line to which it is perpendicular. So if the given line has a slope of , the slope of any line perpendicular to it will have the negative reciprocal of that slope. This gives us:

The graph of  for any real number  is a horizontal line. A line parallel to it is a vertical line, which has a slope that is undefined.

Assume Statement 1 alone. In order to determine the slope of a line on the coordinate plane, the coordinates of two of its points are needed. The -intercept of the line of the equation can be found by substituting  and solving for :

The -intercept of the line is at the origin, . It follows that the -intercept is also at the origin. Therefore, Statement 1 only gives one point on the line, and its slope cannot be determined.

Assume Statement 2 alone. The slope of the line of the equation  can be calculated by putting it in slope-intercept form :

The slope of this line is the coefficient of , which is . A line perpendicular to this one has as its slope the opposite of the reciprocal of , which is

.

The question is answered.

The slope of the first line, in terms of , is 

The slope of the second line is

The slopes of two perpendicular lines have product , so we set up this equation and solve for :

or 

We can eliminate the choice  immediately since the slopes of two perpendicular lines cannot have the same sign. We can also eliminate  and undefined, , since a line with slope 0 and a line with undefined slope are perpendicular to each other, not a line of slope -1 or 1. 

Of the two remaining choices, we check for the choice that includes two numbers whose product is -1. 

 and 

so  is the correct choice.

In order for one line to be perpendicular to another, its slope must be the negative reciprocal of that line's slope. That is, the slope of any perpendicular line must be opposite in sign and the inverse of the slope of the line to which it is perpendicular:

In the given line we can see that   ,  so the slope of any line perpendicular to it will be:

There is only one answer choice with this slope, so we know the following line is perpendicular to the line given in the problem:

For a given line  defined by the equation  with slope , any line perpendicular to  has a slope of , or the negative reciprocal of . Since the slope of the provided line  in this instance is , then the slope of any line perpendicular to  is .

For a given line  defined by the equation  with slope , any line perpendicular to  has a slope of , or the negative reciprocal of . Since the slope of the provided line  in this instance is , then the slope of any line perpendicular to  is .

For a given line  defined by the equation  with slope , any line perpendicular to  has a slope of , or the negative reciprocal of . Since the slope of the provided line  in this instance is , then the slope of any line perpendicular to  is .