Equations of Lines - Algebra
Card 0 of 6030
Find the slope of a line that is perpendicular to a line with the equation 
.
Find the slope of a line that is perpendicular to a line with the equation
Lines can be written in the slope-intercept form:
In this equation, 
is the slope and 
is the y-intercept.
Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. This means that you need to flip the numerator and denominator of the given slope and then change the sign.
The reciprocal of 
is 
; therefore, the reciprocal of 
is 
.
Next, change the sign.
Lines can be written in the slope-intercept form:
In this equation,
Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. This means that you need to flip the numerator and denominator of the given slope and then change the sign.
The reciprocal of
Next, change the sign.
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Given the line 4y = 2x + 1, what is the slope of this line?
Given the line 4y = 2x + 1, what is the slope of this line?
4y = 2x + 1 becomes y = 0.5x + 0.25. We can read the coefficient of x, which is the slope of the line.
4y = 2x + 1
(4y)/4 = (2x)/4 + (1)/4
y = 0.5x + 0.25
y = mx + b, where the slope is equal to m.
The coefficient is 0.5, so the slope is 1/2.
4y = 2x + 1 becomes y = 0.5x + 0.25. We can read the coefficient of x, which is the slope of the line.
4y = 2x + 1
(4y)/4 = (2x)/4 + (1)/4
y = 0.5x + 0.25
y = mx + b, where the slope is equal to m.
The coefficient is 0.5, so the slope is 1/2.
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If (1,2) and (4,6) are on the same line, what is the slope of the line?
If (1,2) and (4,6) are on the same line, what is the slope of the line?
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What is the slope of the line that goes through the points 
?
What is the slope of the line that goes through the points
The slope of a line is given by the following equation:
For the line in question,
The slope of a line is given by the following equation:
For the line in question,
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Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
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
Compare your answer with the correct one above
Which of the following equations describes a line perpendicular to the line 
?
Which of the following equations describes a line perpendicular to the line
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:
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:
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
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
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
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
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
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.
Compare your answer with the correct one above
Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
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
Compare your answer with the correct one above
Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
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
Compare your answer with the correct one above
Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
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
Compare your answer with the correct one above
Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
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
Compare your answer with the correct one above
Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
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
Compare your answer with the correct one above
Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
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
Compare your answer with the correct one above
Find a line perpendicular to the line with the equation:
Find a line perpendicular to the line with the equation:
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
Compare your answer with the correct one above