The slope must be the negative reciprocal and the line must pass through the point (3,2).  So the slope becomes  and this is plugged into  to solve for the -intercept.

Perpendicular lines have slopes that are negative inverses of each other. Since the original equation has a slope of , the perpendicular line must have a slope of . The only other equation with a slope of  is .

First, convert given equation to the slope-intercept form.

In this format, we can tell that the slope is . The slope of a perpendicular line will be the negative reciprocal, making .

Next, substitute the slope into the slope-intercept form to get the intercept, using the point give in the question.

The perpendicular equation becomes . This equation can be re-written in the format of the asnwer chocies.

, or

Perpendicular lines have slopes that are negative reciprocals of one another. The slope of the given line is 9, so a line that is perpendicular to it must have a slope equivalent to its negative reciprocal, which is .

Perpendicular lines have slopes that are negative reciprocals of each other. The given line has a slope of . The negative reciprocal of is , so the perpendicular line must have a slope of . The only line with a slope of is .

To find the equation of a line, we need to know the slope and a point that passes through the line.  Once we know this, we can use the equation  where m is the slope of the line, and  is a point on the line.  For perpendicular lines, the slopes are negative reciprocals of each other.  The slope of  is 5, so the slope of the perpendicular line will have a slope of .  We know that the perpendicular line needs to contain the point (5,3), so we have all of the information we need.  We can now use the equation  

The equation of a line is written in the following format: 

1) The first step, then, is to find the slope, .

 is equal to the change in  divided by the change in .

So,

2) The perpendicular slope of a line with a slope of 2 is the opposite reciprocal of 2, which is .

3) Next step is to find . We don't need to find the equation of the original line; all we need from the original line is the slope. So all we need for is the perpendicular line. We can find values for  and  from the one point we have from the perpendicular line, plug them in, and solve for .

Our point is (4,7)

So, 

Then we just fill in our value for , and we have  as a function of .

This problem first relies on the knowledge of the slope-intercept form of a line, , where m is the slope and b is the y-intercept.

In order for a line to be perpendicular to another line, its slope has to be the negative reciprocal. In this case, we are seeking a line to be perpendicular to . This line has a slope of 2, a.k.a. . This means that the negative reciprocal slope will be . We are told that the y-intercept of this new line is 4.

We can now put these two new pieces of information into to get the equation

.

To solve this type of problem, we have to be familiar with the slope-intercept form of a line, where m is the slope and b is the y-intercept. The line that our line is perpendicular to has the slope-intercept equation , which means that the slope is .

The slope of a perpendicular line would be the negative reciprocal, so our slope is .

We don't know the y-intercept of our line yet, so we can only write the equation as:

.

We do know that the point is on this line, so to solve for b we can plug in -2 for x and 3 for y:

First we can multiply to get .

This makes our equation now:

either by subtracting 3 from both sides, or just by looking at this critically, we can see that b = 0.

Our original becomes , or simply .