Perependicular lines have slopes whose product is .

 and so the answer is 

To find the slope of a perpendicular line, we take the reciprocal  of the known slope , where . 

The easy way to do this is to simply take the fraction (a whole slope can be made into a fraction by placing  in the denominator), exchange the numerator and denominator, then multiply the fraction by 

However, if we attempt to follow this procedure, we get:

, which is undefined.

Thus, our perpendicular line (which is a vertical line) has an undefined slope.

To find the slope of a perpendicular line, we take the reciprocal  of the known slope , where . 

The easy way to do this is to simply take the fraction (a whole slope can be made into a fraction by placing  in the denominator), exchange the numerator and denominator, then multiply the fraction by  Thus,

.

Perpendicular lines will have slopes that are negative reciprocals of one another. Our first step will be to find the slope of the given line by putting the equation into slope-intercept form.

The slope of this line is .

First let's find the negative of the current slope.

Now, we need to find the reciprocal of . In order to find the reciprocal of a number we divide one by that number; therefore, we can calculate the following:

The negative reciprocal will be   or  which will be the slope of the perpendicular line.

Perpendicular lines will have slopes that are negative reciprocals of one another. Our first step will be to find the slope of the given line by putting the equation into slope-intercept form.

The slope of this line is . The negative reciprocal will be , which will be the slope of the perpendicular line.

Now we need to find the answer choice with this slope by converting to slope-intercept form.

This equation has a slope of , and must be our answer.

When determining if a two lines are perpindicular, we are only concerned about their slopes. Consider the basic equation of a line, , where m is the slope of the line. Two lines are perpindicular to each other if one slope is the negative and reciprocal of the other.

The first step of this problem is to get it into the form, , which is . Now we know that the slope, m, is . The reciprocal of that is , and the negative of that is . Therefore, any line that has a slope of  will be perpindicular to the original line.

First we must recognize that the equation is given in slope-intercept form,  where  is the slope of the line.

Two lines are perpendicular if and only if the product of their slopes is . In other words, the slope of a line that is perpendicular to a given line is the negative reciprocal of that slope.

Thus, for a line with a given slope of 3, the line perpendicular to that slope must be the negative reciprocal of 3, or .

To double check that that does indeed give a product of  when multiplied by three simply compute the product: 

Perpendicular lines have slopes whose product is .

The slope is controlled by the coefficient,  from the genral form of the slope-intercept equation: 

Thus the two lines are perpendicular because:

 has 

and

 has 

which when multiplied together results in,

.

For two lines to be perpendicular, their slopes have to have a product of . Find the slopes by the coefficient in front of the .

 and so the two lines are perpendicular. The y-intercept does not matter for determine perpendicularity.

If the slopes of two lines can be calculated, an easy way to determine whether they are perpendicular is to multiply their slopes. If the product of the slopes is , then the lines are perpendicular.

In this case, the slope of the line  is  and the slope of the line  is .

Since , the slopes are not perpendicular.