The slope of a line is 1/3, what is the slope of a line perpendicular to this line

Q: How do you find the reciprocal slope?

We have to get the opposite slope, so the line stands up more than it lies down, but we also have to make it negative, so it goes downhill if the first line went uphill. A line where m = 1 2 m = 1 2 is a positive slope (going uphill). Lines perpendicular to that will have reciprocal slopes.

The slope of a line perpendicular to one with the slope of #1/3# is #-3#. See explanation.

Table of Contents Show

#m_1xxm_2=-1#
What is the slope of the line perpendicular to it?
How do you know if a line is perpendicular to itself?
What happens if you know the slope of a line?
How do you find the reciprocal slope?
What does a slope of 1/3 mean?
What is the slope to a perpendicular line?
What is the equation of a line if the slope is 1 3?

Explanation:

If two lines are perpendicular, then the product of their slopes equals to #-1#. So if one of the slopes is #1/3#, then we can calculate the second slope using the formula:

#m_1xxm_2=-1#

Here we have:

#1/3xxm_2=-1#

#m_2=-3#

Explanation:

Perpendicular slopes are opposite reciprocals of each other.

Opposites: positive vs negative

The perpendicular slope of a positive slope must be negative, and vice versa.

Reciprocals: multiplicative inverses (the numbers will multiply to 1)

Examples of reciprocals:

#2, 1/2 rarr##2*1/2=1#

#1/3, 3 rarr##1/3*3=1#

The opposite of #1/3# is #-1/3#, the reciprocal of #-1/3# is #-3#.

What is the slope of the line perpendicular to it?

If you know the slope of a line, any line perpendicular to it will have a slope equal to the negative inverse of the known slope. Perpendicular means the lines form a 90° angle when they intersect. Say you have a line with a slope of -4. What is the slope of the line perpendicular to it?

How do you know if a line is perpendicular to itself?

If you know the slope of a line, any line parallel to it will have the same slope and these lines will never intersect. If you know the slope of a line, any line perpendicular to it will have a slope equal to the negative inverse of the known slope. Perpendicular means the lines form a 90° angle when they intersect.

What happens if you know the slope of a line?

How do you find the reciprocal slope?

We have to get the opposite slope, so the line "stands up" more than it "lies down," but we also have to make it negative, so it goes downhill if the first line went uphill. A line where m = 1 2 m = 1 2 is a positive slope (going uphill). Lines perpendicular to that will have reciprocal slopes.