How to find out if lines are perpendicular - Math
Card 1 of 321
Which of the following are perpendicular to the line with the formula 
?
I.
II. 
III. 
Which of the following are perpendicular to the line with the formula
I.
II.
III.
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The slope of a perpendicular line is equal to the negative reciprocal of the original line. This means that the slope of our perpendicular line must be 3. We can also note that 
is also equal to 3, so both of these slopes are correct. The y-intercept does not matter, as the slope is the only thing that determines the slant of the line. Therefore, numerals I and III are both correct.
The slope of a perpendicular line is equal to the negative reciprocal of the original line. This means that the slope of our perpendicular line must be 3. We can also note that
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Which of the following lines is perpendicular to 
?
Which of the following lines is perpendicular to
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In order for two lines to be perpendicular to each other, their slopes must be opposites and reciprocals of each other, meaning the fraction must be flipped upside down and the signs must be changed. In this situation, the original equation had a slope of 
, so the perpendicular slope must be 
.
In order for two lines to be perpendicular to each other, their slopes must be opposites and reciprocals of each other, meaning the fraction must be flipped upside down and the signs must be changed. In this situation, the original equation had a slope of
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Which of the following lines will be perpendicular to 
?
Which of the following lines will be perpendicular to
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Two lines are perpendicular if they have opposite reciprocal slopes. When a line is in standard 
form, the 
is the slope. A perpendicular line will have a slope of 
.
The slope of our given line is 
. Therefore we want a slope of 
. The only line with the correct slope is 
.
Two lines are perpendicular if they have opposite reciprocal slopes. When a line is in standard
The slope of our given line is
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Which of the following are perpendicular to the line with the formula ?
I.
II.
III.
Which of the following are perpendicular to the line with the formula
I.
II.
III.
Tap to reveal answer
The slope of a perpendicular line is equal to the negative reciprocal of the original line. This means that the slope of our perpendicular line must be 3. We can also note that is also equal to 3, so both of these slopes are correct. The y-intercept does not matter, as the slope is the only thing that determines the slant of the line. Therefore, numerals I and III are both correct.
The slope of a perpendicular line is equal to the negative reciprocal of the original line. This means that the slope of our perpendicular line must be 3. We can also note that
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Which of the following lines is perpendicular to ?
Which of the following lines is perpendicular to
Tap to reveal answer
In order for two lines to be perpendicular to each other, their slopes must be opposites and reciprocals of each other, meaning the fraction must be flipped upside down and the signs must be changed. In this situation, the original equation had a slope of , so the perpendicular slope must be .
In order for two lines to be perpendicular to each other, their slopes must be opposites and reciprocals of each other, meaning the fraction must be flipped upside down and the signs must be changed. In this situation, the original equation had a slope of
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Which of the following lines will be perpendicular to ?
Which of the following lines will be perpendicular to
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Two lines are perpendicular if they have opposite reciprocal slopes. When a line is in standard form, the is the slope. A perpendicular line will have a slope of .
The slope of our given line is . Therefore we want a slope of . The only line with the correct slope is .
Two lines are perpendicular if they have opposite reciprocal slopes. When a line is in standard
The slope of our given line is
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Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
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Lines can be written in the slope-intercept format:
In this format, 
equals the line's slope and 
represents where the line intercepts the y-axis.
In the given equation:
Perpendicular lines have slopes that are negative reciprocals of each other.
First, we need to find its reciprocal.
Second, we need to rewrite it with the opposite sign.
Only one of the choices has a slope of 
.
Lines can be written in the slope-intercept format:
In this format,
In the given equation:
Perpendicular lines have slopes that are negative reciprocals of each other.
First, we need to find its reciprocal.
Second, we need to rewrite it with the opposite sign.
Only one of the choices has a slope of
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Which of the following equations describes a line perpendicular to the line 
?
Which of the following equations describes a line perpendicular to the line
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The line 
is a vertical line. Therefore, a perpendicular line is going to be horizontal and have a slope of zero.
The equation 
is such a line.
The lines 
and 
are both vertical lines, while the lines 
and 
have slopes of 
and 
, respectively.
The line
The equation
The lines
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Which of the following lines could be perpendicular to the following:
Which of the following lines could be perpendicular to the following:
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The only marker for whether lines are perpendicular is whether their slopes are the opposite-reciprocal for the other line's slope. The 
-intercept is not important. Therefore, the line perpendicular to 
will have a slope of 
or 
The only marker for whether lines are perpendicular is whether their slopes are the opposite-reciprocal for the other line's slope. The
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Which ONE of these statements about the lines defined by the following equations is TRUE?
Line 1: 
Line 2: 
Which ONE of these statements about the lines defined by the following equations is TRUE?
Line 1:
Line 2:
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The TRUE statement:
"The lines intersect and are perpendicular." This is true because the slopes of the two lines are opposite-reciprocals of each other.
The FALSE statements:
"The lines intersect at the point 
." The lines actually intersect at the point 
. Neither line touches the point 
, as their y-intercepts are given in their respective equations as 
and 
.
"The slopes of the two lines are identical." This is not true because the slope of Line 1 is 
whereas the slope of Line 2 is 
.
"The lines do not intersect." The lines would need to be parallel (i.e., have the same slope) for this to be the case, but the lines do not have the same slope.
"The lines intersect only once because they are parallel." Parallel lines never intersect, so this statement cannot be made of any set of two lines.
The TRUE statement:
"The lines intersect and are perpendicular." This is true because the slopes of the two lines are opposite-reciprocals of each other.
The FALSE statements:
"The lines intersect at the point
"The slopes of the two lines are identical." This is not true because the slope of Line 1 is
"The lines do not intersect." The lines would need to be parallel (i.e., have the same slope) for this to be the case, but the lines do not have the same slope.
"The lines intersect only once because they are parallel." Parallel lines never intersect, so this statement cannot be made of any set of two lines.
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Which equation describes a line that is perpendicular to 
Which equation describes a line that is perpendicular to
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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
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
The only answer choice with a slope of
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Which of these lines is perpendicular to 
?
Which of these lines is perpendicular to
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Perpendicular lines have slopes that are negative reciprocals of one another. Since all of these lines are in the 
format, it is easy to determine their slopes, or 
.
The slope of the original line is 
, so any line that is perpendicular to it must have a slope of 
.
The only line with a slope of 
is 
.
Perpendicular lines have slopes that are negative reciprocals of one another. Since all of these lines are in the
The slope of the original line is
The only line with a slope of
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Determine if the lines 
and 
are perpendicular.
Determine if the lines
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For lines to be perpendicular, the slopes need to be negative reciprocals of each other. For the line 
, the slope is 1. For a line to be perpendicular to it, it will need to have a slope of 
. Since the line 
has a slope of -1, the lines are perpendicular to each other.
For lines to be perpendicular, the slopes need to be negative reciprocals of each other. For the line
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Which of these lines is perpendicular to
Which of these lines is perpendicular to
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Perpendicular lines have slopes that are negative reciprocals of each other. If you convert the given line to the 
form, you get
which indicates a slope of 
. Thus, the slope of the perpendicular line must be 
, which is the negative reciprocal of 
. The only line with a slope of 
is
.
Perpendicular lines have slopes that are negative reciprocals of each other. If you convert the given line to the
which indicates a slope of
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Which of the following best describes the relationship between the 2 lines 
and 
?
Which of the following best describes the relationship between the 2 lines
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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.
In order to compare these lines, start by transforming the second equation into slope-intercept form:
In this equation, the variable 
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.
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Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
Tap to reveal answer
Lines can be written in the slope-intercept format:
In this format, equals the line's slope and represents where the line intercepts the y-axis.
In the given equation:
Perpendicular lines have slopes that are negative reciprocals of each other.
First, we need to find its reciprocal.
Second, we need to rewrite it with the opposite sign.
Only one of the choices has a slope of 
.
Lines can be written in the slope-intercept format:
In this format,
In the given equation:
Perpendicular lines have slopes that are negative reciprocals of each other.
First, we need to find its reciprocal.
Second, we need to rewrite it with the opposite sign.
Only one of the choices has a slope of
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Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
Tap to reveal answer
Lines can be written in the slope-intercept format:
In this format, equals the line's slope and represents where the line intercepts the y-axis.
In the given equation:
Perpendicular lines have slopes that are negative reciprocals of each other.
First, we need to find its reciprocal.
Second, we need to rewrite it with the opposite sign.
Only one of the choices has a slope of 
.
Lines can be written in the slope-intercept format:
In this format,
In the given equation:
Perpendicular lines have slopes that are negative reciprocals of each other.
First, we need to find its reciprocal.
Second, we need to rewrite it with the opposite sign.
Only one of the choices has a slope of
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Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
Tap to reveal answer
Lines can be written in the slope-intercept format:
In this format, equals the line's slope and represents where the line intercepts the y-axis.
In the given equation:
Perpendicular lines have slopes that are negative reciprocals of each other.
First, we need to find its reciprocal.
Rewrite.
Second, we need to rewrite it with the opposite sign.
Only one of the choices has a slope of 
.
Lines can be written in the slope-intercept format:
In this format,
In the given equation:
Perpendicular lines have slopes that are negative reciprocals of each other.
First, we need to find its reciprocal.
Rewrite.
Second, we need to rewrite it with the opposite sign.
Only one of the choices has a slope of
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Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
Tap to reveal answer
Lines can be written in the slope-intercept format:
In this format, equals the line's slope and represents where the line intercepts the y-axis.
In the given equation:
Perpendicular lines have slopes that are negative reciprocals of each other.
First, we need to find its reciprocal.
Rewrite.
Second, we need to rewrite it with the opposite sign.
Only one of the choices has a slope of 
.
Lines can be written in the slope-intercept format:
In this format,
In the given equation:
Perpendicular lines have slopes that are negative reciprocals of each other.
First, we need to find its reciprocal.
Rewrite.
Second, we need to rewrite it with the opposite sign.
Only one of the choices has a slope of
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Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
Tap to reveal answer
Lines can be written in the slope-intercept format:
In this format, equals the line's slope and represents where the line intercepts the y-axis.
In the given equation:
Perpendicular lines have slopes that are negative reciprocals of each other.
First, we need to find its reciprocal.
Second, we need to rewrite it with the opposite sign.
Only one of the choices has a slope of 
.
Lines can be written in the slope-intercept format:
In this format,
In the given equation:
Perpendicular lines have slopes that are negative reciprocals of each other.
First, we need to find its reciprocal.
Second, we need to rewrite it with the opposite sign.
Only one of the choices has a slope of
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