How to find the slope of a perpendicular line - GRE Quantitative Reasoning
Card 1 of 96
What is the slope of the line perpendicular to the line given by the equation
6x – 9y +14 = 0
What is the slope of the line perpendicular to the line given by the equation
6x – 9y +14 = 0
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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.
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.
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What is the slope of the line perpendicular to the line represented by the equation y = -2x+3?
What is the slope of the line perpendicular to the line represented by the equation y = -2x+3?
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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.
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.
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What is the slope of any line perpendicular to 2_y_ = 4_x_ +3 ?
What is the slope of any line perpendicular to 2_y_ = 4_x_ +3 ?
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First, we must solve the equation for y to determine the slope: y = 2_x_ + 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
First, we must solve the equation for y to determine the slope: y = 2_x_ + 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
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What line is perpendicular to 2x + y = 3 at (1,1)?
What line is perpendicular to 2x + y = 3 at (1,1)?
Tap to reveal answer
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.
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.
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What is the slope of a line perpendicular to the following:
What is the slope of a line perpendicular to the following:
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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 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.
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A line is defined by the following equation:
What is the slope of a line that is perpendicular to the line above?
A line is defined by the following equation:
What is the slope of a line that is perpendicular to the line above?
Tap to reveal answer
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 
The equation of a line is
Rearrange the equation to match this:
For the perpendicular line, the slope is the negative reciprocal;
therefore
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Find the slope of a line perpendicular to the line y = –3x – 4.
Find the slope of a line perpendicular to the line y = –3x – 4.
Tap to reveal answer
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.
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.
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What is the slope of a line perpendicular to line passing through the points (5, 7) and (2, 12)?
What is the slope of a line perpendicular to line passing through the points (5, 7) and (2, 12)?
Tap to reveal answer
We find the slope of a perpendicular line by taking the opposite and reciprocal of our given line's slope; therefore, we must first solve for the slope of our line. Given our points, we must find the ratio of the rise to the run, that is:
slope = rise/run = (y2 – y1)/(x2 – x1)
slope = (7 – 12)/(5 – 2) = –5/3
The perpendicular will be "flipped" (i.e. reciprocal) and also positive (opposite); therefore, it is: 3/5.
We find the slope of a perpendicular line by taking the opposite and reciprocal of our given line's slope; therefore, we must first solve for the slope of our line. Given our points, we must find the ratio of the rise to the run, that is:
slope = rise/run = (y2 – y1)/(x2 – x1)
slope = (7 – 12)/(5 – 2) = –5/3
The perpendicular will be "flipped" (i.e. reciprocal) and also positive (opposite); therefore, it is: 3/5.
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Which of the following lines has a slope perpendicular to the line 3x+4y=10?
Which of the following lines has a slope perpendicular to the line 3x+4y=10?
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The slope of the original equation is -$\frac{3}{4}$. (This can be found by transforming into the form y=mx+b, yielding y=-$\frac{3}{4}$x+\frac{5}{2}$.
Thus, the slope of any perpendicular line will be $\frac{4}{3}$.
The slope of the original equation is -$\frac{3}{4}$. (This can be found by transforming into the form y=mx+b, yielding y=-$\frac{3}{4}$x+\frac{5}{2}$.
Thus, the slope of any perpendicular line will be $\frac{4}{3}$.
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A line in the x-y plane passes through the points (3,5) and (–2, 4). Another line does not pass through the origin, and does not have the same intercept as the first line. If the two lines are perpendicular, what is the slope of the second line?
A line in the x-y plane passes through the points (3,5) and (–2, 4). Another line does not pass through the origin, and does not have the same intercept as the first line. If the two lines are perpendicular, what is the slope of the second line?
Tap to reveal answer
Disregard the information about the second line not passig through the origin and not having a particular intercept—it is largely irrelevant.
The important information is the fact that the second line, as mentioned, is perpendicular to the first. This means that its slope is the negative reciprocal of the slope of the first line.
We can find the slope of the first line using the slope formula and our two points, (3,5) and (–2, 4).
The slope of the second line is the negative reciprocal of 
, meaning it must be 
.
Disregard the information about the second line not passig through the origin and not having a particular intercept—it is largely irrelevant.
The important information is the fact that the second line, as mentioned, is perpendicular to the first. This means that its slope is the negative reciprocal of the slope of the first line.
We can find the slope of the first line using the slope formula and our two points, (3,5) and (–2, 4).
The slope of the second line is the negative reciprocal of
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Which of the following represents a line that is perpendicular to the equation 
?
Which of the following represents a line that is perpendicular to the equation
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Begin by putting the original equation into the form of 
:
To find a line that is perpendicular to the above, take the slope, find the reciprocal, and change the sign on it. In other words, since our slope is 6, a line that is perpendicular will have an 
-value of 
.
Now go through each answer choice and put it into the form of 
. The correct answer will be the one with an 
-value of 
.
In this case, it will be the equation 
Begin by putting the original equation into the form of
To find a line that is perpendicular to the above, take the slope, find the reciprocal, and change the sign on it. In other words, since our slope is 6, a line that is perpendicular will have an
Now go through each answer choice and put it into the form of
In this case, it will be the equation
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The equation of a particular line is as follows:
.
What is the slope of a line perpendicuar to this one?
The equation of a particular line is as follows:
What is the slope of a line perpendicuar to this one?
Tap to reveal answer
The slope of a perpendicular line is the opposite reciporical of the originial slope.
The opposite would be changing the sign from positive to negative or vice versa.
The reciporical is flipping the fraction or switching the numerator and denominator.
This equation is in slope-intercept form,
meaning m represents the slope of the equation.
Since the original is 
, then the perpendicular would be positive and would swtich the 7 and 3 giving us 
.
The slope of a perpendicular line is the opposite reciporical of the originial slope.
The opposite would be changing the sign from positive to negative or vice versa.
The reciporical is flipping the fraction or switching the numerator and denominator.
This equation is in slope-intercept form,
meaning m represents the slope of the equation.
Since the original is
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What is the slope of any line perpendicular to 2_y_ = 4_x_ +3 ?
What is the slope of any line perpendicular to 2_y_ = 4_x_ +3 ?
Tap to reveal answer
First, we must solve the equation for y to determine the slope: y = 2_x_ + 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
First, we must solve the equation for y to determine the slope: y = 2_x_ + 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
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What line is perpendicular to 2x + y = 3 at (1,1)?
What line is perpendicular to 2x + y = 3 at (1,1)?
Tap to reveal answer
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.
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.
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What is the slope of the line perpendicular to the line given by the equation
6x – 9y +14 = 0
What is the slope of the line perpendicular to the line given by the equation
6x – 9y +14 = 0
Tap to reveal answer
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.
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.
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What is the slope of the line perpendicular to the line represented by the equation y = -2x+3?
What is the slope of the line perpendicular to the line represented by the equation y = -2x+3?
Tap to reveal answer
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.
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.
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What is the slope of a line perpendicular to the following:
What is the slope of a line perpendicular to the following:
Tap to reveal answer
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 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.
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A line is defined by the following equation:
What is the slope of a line that is perpendicular to the line above?
A line is defined by the following equation:
What is the slope of a line that is perpendicular to the line above?
Tap to reveal answer
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
The equation of a line is
Rearrange the equation to match this:
For the perpendicular line, the slope is the negative reciprocal;
therefore
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Find the slope of a line perpendicular to the line y = –3x – 4.
Find the slope of a line perpendicular to the line y = –3x – 4.
Tap to reveal answer
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.
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.
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What is the slope of a line perpendicular to line passing through the points (5, 7) and (2, 12)?
What is the slope of a line perpendicular to line passing through the points (5, 7) and (2, 12)?
Tap to reveal answer
We find the slope of a perpendicular line by taking the opposite and reciprocal of our given line's slope; therefore, we must first solve for the slope of our line. Given our points, we must find the ratio of the rise to the run, that is:
slope = rise/run = (y2 – y1)/(x2 – x1)
slope = (7 – 12)/(5 – 2) = –5/3
The perpendicular will be "flipped" (i.e. reciprocal) and also positive (opposite); therefore, it is: 3/5.
We find the slope of a perpendicular line by taking the opposite and reciprocal of our given line's slope; therefore, we must first solve for the slope of our line. Given our points, we must find the ratio of the rise to the run, that is:
slope = rise/run = (y2 – y1)/(x2 – x1)
slope = (7 – 12)/(5 – 2) = –5/3
The perpendicular will be "flipped" (i.e. reciprocal) and also positive (opposite); therefore, it is: 3/5.
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