Two lines are perpendicular if they have slopes that are opposite reciprocals of each other (opposite:  different signs, reciprocal:  switch the numerator and denominator). 

To find the slope of a line, we write it in slope-intercept form

where m is the slope.

Given the equation

we will solve for y by dividing each term by -3.  

We can see that the slope of this line is 3.  The slope of a line perpendicular to this one will have a slope of .  

Therefore, the line

is perpendicular to the original line.

In order to compare these lines, start by transforming the second equation into slope-intercept form:

In this equation, the variable  represents the slope. Identify the slope of the second line's equation by transforming it until y-variable is isolated on the left side.

First, we will add 8 to both sides of the equation.

Divide both sides of the equation by -2.

Rearrange and simplify.

This means that the second line possesses the following slope:

.

We know that the slope of the first line is 2; therefore, the slope of the second line is the negative reciprocal of the first. Perpendicular lines have slopes that are negative reciprocals of one another. 

To find a line that is perpendicular to another line, the slopes must be opposite reciprocals of each other. "Opposite" means there is a sign change, and "reciprocal" means that the numerator and denominator are inverted.  

For example, the following are opposite reciprocals of each other:

First, convert the equation to slope-intercept form:

The slope is   To find a line that is perpendicular, find a line with a slope that is the opposite reciprocal of , or .

Looking at the equation

convert the equation to slope-intercept form.

The slope is , making it perpendicular to the original line.

To find out if two lines are perpendicular, we just need to see whether their slopes are opposite reciprocals of each other.

The reciprocal of 6 is , so the opposite reciprocal is .

The only answer choice with a slope of  is

First, you should put the equation in slope intercept form (y = mx + b), where m is the slope.  

10x + 4y = 20

Isolate the y term

10x + 4y – 10x = 20 – 10x

4y = 20 – 10x

Rearrange the terms

4y = –10x + 20

Divide both sides by 4

The slope of the given line is –10/4. A perpendicular line will have a slope with the opposite reciprocal. In simpler terms, you flip the slope and change the sign, therefore, the opposite reciprocal is 4/10.

The slope of the line that contains the points (1, 9) and (3, 4) is .

The negative reciprocal is , which is the slope of the perpendicular line.

Slope of lines that are perpendicular to each other are the negative reciprocal.

Perpendicular lines have slopes that are negative reciprocals of one another. Since the original line has a slope of , the perpendicular line must have a slope of .

Perpendicular lines have slopes that are negative reciprocals of one another. The given line's slope is 5, which means that the slope of the other line must be its negative reciprocal. The negative reciprocal of 5 is .

Perpendicular lines have slopes that are negative inverses of one another. The slope of the given line is . The negative inverse of is , which must be the slope of the perpendicular line.