Two lines are perpendicular if and only if their slopes are "negative reciprocals" of each other such as 1/2 and -2. In our problem we are not given line equations that we can readily see the slope, so we must convert each equation to slope intercept form or .

First find out the slope of the given equation by converting it to slope-intercept form:

So we need a line whose slope is the negative reciprocal of -1/8 (which is 8). Even though this number is not "negative" the idea of the negative reicprocal gives a positive number here because two negative signs cancel each other to make a positive. ...negative recicprocal....

Now we must choose an equation that, after being changed to slope intercept form has a slope of 8.

So   (answer) is the equation of a line that is perpendicular to 

.

A line is perpendicular to another line when they meet at a degree angle. That angle is the result of the slopes of the lines being opposite reciprocals.

The "opposite reciprocal" of  is best described as .

First we reorganize the original equation to isolate . To do this we want to get our equation into slope intercept form .

First subtract 12 from each side.

Now divide by 4 and simplify where possible.

opposite reciprocal

The only equation in the answer choices with a slope of is

.

This problem can be quickly solved through using the point-slope formula considering the given information. Before we start substituting in values, however, it's important to remember what determines a line to be perpendicular relative to another. By definition, lines are perpendicular if their slopes have a product of . For instance, if a line has a slope of , the line perpendicular to it will have a slope of  because . Using this concept, we must first determine the slope of the perpendicular line. We are given that the reference line has a slope of . That means the perpendicular line must have a slope of  because . Now that we know  (slope) and have a coordinate, we have fulfilled the requirements of the point-slope formula and can begin to substitue in information and solve for the equation. 

Here we arbitrarily use 

Before beginning this problem, it's important to remember what defines a perpendicular line. A line is perpendicular to another if the product of the two lines' slope is  For instance, if a line has a slope of , the line perpendicular to it will have a slope of  because . Using this concept, we must first determine the slope of the perpendicular line. The line of interest is perpendicular to a line with a slope of , therefore its slope must be 

The problem does not provide us enough information to use the point-slope formula to solve for the equation. However, we are provided with the line's y-intercept. This allows us to use the skeleton  to solve for the equation, where  is slope and  is the y-intercept.

By definition, lines are perpendicular if the product of their slopes is . For example, if a line has a slope of , the perpendicular line would have a slope of . This same concept can be used to solve this problem. Beginning with the issue of slope, we realize that the reference slope is . In order to create a product of , we must multiply  by . Therefore, the slope of the perpendicular line is . 

Because the problem has not given us a point, we cannot use the point-slope formula to solve for the equation. However, we have been provided with the line's y-intercept. With this information, we are ready to construct the line's equation remembering the  skeleton. We have  and now we have . Substituting in the given information will yield our answer. 

Because  is usally not written in front of variables, we may omit it from the final answer. 

Begin by calculating the slope of Line 1 as 

.

Now, realize that since Line 2 is perpindicular to Line 1, the slope of Line 2 is the negative reciprocal of the slope of Line 1.

Therefore, the slope of Line 2 is given as 

.

We also know that Line 2 passes through point (8,5).

Therefore, we may use "point-slope" form to express the equation of Line 2 as: 

.

Finally, convert this "point-slope" equation to "slope-intercept" form in order to match the result with the correct answer choice: 

. 

When finding the slope of a perpendicular line, we need to ensure we have  form.    stands for slope. Our  is . To find the perpendicular slope, we need to take the negative reciprocal of that value which is . Since we are looking for an equation, we need to reuse the  form to solve for  . We do this by plugging in our coordinates. 

 Add  on both sides.

Our equation is now .

When finding the slope of a perpendicular line, we need to ensure we have  form.  Let's rearrange it. By subtracting  on both sides and dividing  on both sides, we get .  stands for slope. Our  is . To find the perpendicular slope, we need to take the negative reciprocal of that value which is . Since we are looking for an equation, we need to reuse the  form to solve for  . We do this by plugging in our coordinates. 

 Subtract  on both sides.

Our equation is now .

When finding the slope of a perpendicular line, we need to ensure we have  form.  Let's rearrange it. By add  on both sides and dividing  on both sides, we get .  stands for slope. Our  is . To find the perpendicular slope, we need to take the negative reciprocal of that value which is . Since we are looking for an equation, we need to reuse the  form to solve for  . We do this by plugging in our coordinates. 

 Add  on both sides.

Our equation is now .

Perpendicular lines have slopes that are opposite reciprocals meaning that the slope is flpped. The equation that satisfies both of these criteria is: