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.

First we must find the slope of the given line. The slope of y = –3x – 4 is –3. The slope of the perpendicular line is the negative reciprocal. This means you change the sign of the slope to its opposite: in this case to 3. Then find the reciprocal by switching the denominator and numerator to get 1/3; therefore the slope of the perpendicular line is 1/3.

The question puts the line in point-slope form y – y₁ = m(x – x₁), where m is the slope. Therefore, the slope of the original line is 1/2.  A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of the original line is –2, and is thus the slope of its perpendicular line. 

The equation of a line is  where  is the slope.

Rearrange the equation to match this:

For the perpendicular line, the slope is the negative reciprocal;

therefore 

A slope perpendicular to another line can be found by taking the reciprocal of the orignal slope and changing the sign.

If you solve for  in the given equation,

divide by three on each side

.

There is a slope of  because the equation is in slope-intercept form where m represents the slope,

.

The reciprocal of that with a changed sign is

.

The line  is a vertical line.  The line perpendicular to a vertical line must always have a slope of zero.  

The only valid answer with a slope of zero is:   

Let's write the equation of the given line in slope-intercept form.

The slope of the given line is expressed by the coefficient of x. The slope here is .

To find the slope of the perpendicular line, we take the negative reciprocal of the given line's slope. Therefore, the slope of the perpendicular line is .