The equation  is a vertical line on the coordinate plane. Any line perpendicular to a vertical line is a horizontal line. Horizontal lines have slopes of zero.

The correct answer is .

Write the slope formula and find the slope of the first line.

The slope of the perpendicular line is the negative reciprocal of the original slope.

Therefore, the slope of the perpendicular line is .

The slope of a line perpendicular is the negative reciprocal of the given line.

Since the given slope is calculated as , then the slope of the perpendicular line would be  .

The slope of the given line is 3. The slope of a perpendicular line is the negative inverse of the given line. In this case, that is equal to . Therefore, the correct answer is:

When looking at the equation of the given line, we know that the slope is  and the y-intercept is . Any line perpendicular to the given line will create a 90 degree angle with the given line.

Now, there are INFINITE lines perpendicular to the given line, all with different y-intercepts. So in other words, the line we are looking for will have no dependence on the y-intercept, as any y-intercept will do. What we do care about is the slope of the line.

The slope of any line perpendicular to a given line has a negative reciprocal of the slope. So for this problem:

The only line that has this slope is

Parallel lines will never touch, and therefore they must have the same slope.

Many of the answers are reciprocals or negative slopes, but the slope we are looking for is .

That leaves us with 2 answers. However, one of the answers is the exact same equation for a line as the given equation. Therefore our answer is:

Two lines are perpendicular if and only if their slopes are negative reciprocals. To find the slope, we must put the equation into slope-intercept form,  , where  equals the slope of the line. We begin by subtracting  from each side, giving us . Next, we subtract 32 from each side, giving us . Finally, we divide each side by , giving us . We can now see that the slope is . Therefore, any line perpendicular to  must have a slope of . Of the equations above, only  has a slope of .

Convert the given equation to slope-intercept form: 

Divide both sides of the equation by :

The slope of this function is :  

The slope of the perpendicular line will be the negative reciprocal of the original slope. Substitute and solve:

Only  has a slope of .

Two perpendicular lines have slopes that are opposite reciprocals, meaning that the sign changes and the reciprocal of the slope is taken. 

The original equation is in slope-intercept form,

 where  represents the slope.

In this case, the slope of the original is: 

After taking the opposite reciprocal, the result is the slope below: 

Any equation of the form , such as , can be graphed by a vertical line; any equation of the form , such as , can be graphed  by a horizontal line. A vertical line and a horizontal line are perpendicular to each other.