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.

Write each equation in the slope-intercept form  by solving for ; the -coefficient  is the slope of the line.

Subtract  from both sides:

The line of this equation has slope .

Subtract  from both sides:

Multiply both sides by 

The line of this equation has slope .

Two lines are parallel if and only if they have the same slope; this is not the case. They are perpendicular if and only if the product of their slopes is ; this is not the case, since

.

The correct response is that the lines are neither parallel nor perpendicular.

Write each equation in the slope-intercept form  by solving for ; the -coefficient  is the slope of the line.

Subtract  from both sides:

Multiply both sides by :

The slope is the -coefficient 

Add  to both sides:

Multiply both sides by :

The slope is the -coefficient .

Two lines are parallel if and only if they have the same slope; this is not the case. They are perpendicular if and only if the product of their slopes is ; this is not the case, since . The lines are neither parallel nor perpendicular.

Two lines on the coordinate plane are perpendicular if and only if the product of their slopes is . The product of the slopes of the lines in question is

,

so the lines are indeed perpendicular.