Since a perpendicular line has a slope that is the negative reciprocal of the original line, the new slope is . There is only one answer with the correct slope.

First, find the slope of the original line, which is . You can do this by isolating for  so that the equation is in slope-intercept form. Once you find the slope, just replace the  in the original equation withe the negative reciprocal (perpendicular lines have a negative reciprocal slope for each other). Thus, your answer is 

In order for two lines to be perpendicular, their slopes must be opposites and recipricals of each other. The first step is to find the slope of the given equation:

Therefore, the slope of the perpendicular line must be . Using the point-slope formula, we can find the equation of the new line:

Perdendicular lines have slopes that are opposite reciprocals.  The slope of the old line is , so the new slope is .

Plug the new slope and the given point into the slope intercept equation to calculate the intercept:

or , so .

Thus , or .

First, calculate the slope of the line segment between the given points.

We want a line that is perpendicular to this segment and passes through its midpoint. The slope of a perpendicular line is the negative inverse. The slope of the perpendicular bisector will be .

Next, we need to find the midpoint of the segment, using the midpoint formula.

Using the midpoint and the slope, we can solve for the value of the y-intercept.

Using this value, we can write the equation for the perpendicular bisector in slope-intercept form.

The equation is given in the slope-intercept form, so we know the slope is .  To have perpendicular lines, the new slope must be the opposite reciprocal of the old slope, or

Then plug the new slope and the point into the slope-intercept form of the equation:

so so  

So the new equation becomes:  and in standard form

The original line has a slope of , a line perpendicular to the original line will have a slope which is the negative reciprocal of this value.

Perpendicular lines have slopes that are the opposite reciprocals of each other. Thus, we first identify the slope of the given line, which is  (since it is in the form , where  represents slope).

Then, we know that any line which is perpendicular to this will have a slope of .

Thus, we can determine that  is the only choice with the correct slope. 

In standard form, the is the slope.

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

For our given line, the slope is . Therefore, the slope of the perpendicular line is .

The definition of perpendicular lines is that their slopes are inverse reciprocals of one another. Since the slope in the given equation is , this means that the slope of its perpendicular line would be .

The answer 

is the only equation listed that has a slope of .