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.

If lines are perpendicular, then their slopes will be negative reciprocals.

First, we need to find the slope of the given line.

Because we know that our given line's slope is , the slope of the line perpendicular to it must be .

We find the slope of a perpendicular line by taking the opposite and reciprocal of our given line's slope; therefore, we must first solve for the slope of our line. Given our points, we must find the ratio of the rise to the run, that is:

slope = rise/run = (y₂ – y₁)/(x₂ – x₁)

slope = (7 – 12)/(5 – 2) = –5/3

The perpendicular will be "flipped" (i.e. reciprocal) and also positive (opposite); therefore, it is: 3/5.

The slope of the original equation is . (This can be found by transforming into the form , yielding .

Thus, the slope of any perpendicular line will be . 

Disregard the information about the second line not passig through the origin and not having a particular intercept—it is largely irrelevant.

The important information is the fact that the second line, as mentioned, is perpendicular to the first. This means that its slope is the negative reciprocal of the slope of the first line.

We can find the slope of the first line using the slope formula and our two points, (3,5) and (–2, 4).

The slope of the second line is the negative reciprocal of , meaning it must be .

Begin by putting the original equation into the form of :

To find a line that is perpendicular to the above, take the slope, find the reciprocal, and change the sign on it. In other words, since our slope is 6, a line that is perpendicular will have an -value of .

Now go through each answer choice and put it into the form of . The correct answer will be the one with an -value of .

In this case, it will be the equation 

First, we must solve the equation for y to determine the slope:  y = 2x + ³/₂

By looking at the coefficient in front of x, we know that the slope of this line has a value of 2. To fine the slope of any line perpendicular to this one, we take the negative reciprocal of it:

slope = m , perpendicular slope = – ¹/_m

slope = 2 , perpendicular slope = – ¹/₂

Find the slope of the given line.  The perpendicular slope will be the opposite reciprocal of the original slope.  Use the slope-intercept form (y = mx + b) and substitute in the given point and the new slope to find the intercept, b.  Convert back to standard form of an equation:  ax + by =  c.

First rearrange the equation so that it is in slope-intercept form, resulting in y=2/3 x + 14/9. The slope of this line is 2/3, so the slope of the line perpendicular will have the opposite reciprocal as a slope, which is -3/2.

Perpendicular lines have slopes that are the opposite of the reciprocal of each other. In this case, the slope of the first line is -2. The reciprocal of -2 is -1/2, so the opposite of the reciprocal is therefore 1/2.