How to find the equation of a perpendicular line - SSAT Upper Level Quantitative
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What is the equation of a line that runs perpendicular to the line 2_x_ + y = 5 and passes through the point (2,7)?
What is the equation of a line that runs perpendicular to the line 2_x_ + y = 5 and passes through the point (2,7)?
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First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2_x_ +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2_x_ + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½_x_ + 6. Rearranged, it is –x/2 + y = 6.
First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2_x_ +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2_x_ + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½_x_ + 6. Rearranged, it is –x/2 + y = 6.
Which of the following equations represents a line that goes through the point 
and is perpendicular to the line 
?
Which of the following equations represents a line that goes through the point 
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In order to solve this problem, we need first to transform the equation from standard form to slope-intercept form:
Transform the original equation to find its slope.
First, subtract 
from both sides of the equation.
Simplify and rearrange.
Next, divide both sides of the equation by 6.
The slope of our first line is equal to 
. Perpendicular lines have slopes that are opposite reciprocals of each other; therefore, if the slope of one is x, then the slope of the other is equal to the following:
Let's calculate the opposite reciprocal of our slope:
The slope of our line is equal to 2. We now have the following partial equation:
We are missing the y-intercept, 
. Substitute the x- and y-values in the given point 
to solve for the missing y-intercept.
Add 4 to both sides of the equation.
Substitute this value into our partial equation to construct the equation of our line:
In order to solve this problem, we need first to transform the equation from standard form to slope-intercept form:
Transform the original equation to find its slope.
First, subtract 
Simplify and rearrange.
Next, divide both sides of the equation by 6.
The slope of our first line is equal to 
Let's calculate the opposite reciprocal of our slope:
The slope of our line is equal to 2. We now have the following partial equation:
We are missing the y-intercept, 
Add 4 to both sides of the equation.
Substitute this value into our partial equation to construct the equation of our line:
Line m passes through the points (1, 4) and (5, 2). If line p is perpendicular to m, then which of the following could represent the equation for p?
Line m passes through the points (1, 4) and (5, 2). If line p is perpendicular to m, then which of the following could represent the equation for p?
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The slope of m is equal to y2-y1/x2-x1 = 2-4/5-1 = -1/2
Since line p is perpendicular to line m, this means that the products of the slopes of p and m must be **–**1:
(slope of p) * (-1/2) = -1
Slope of p = 2
So we must choose the equation that has a slope of 2. If we rewrite the equations in point-slope form (y = mx + b), we see that the equation 2x – y = 3 could be written as y = 2x – 3. This means that the slope of the line 2x – y =3 would be 2, so it could be the equation of line p. The answer is 2x – y = 3.
The slope of m is equal to y2-y1/x2-x1 = 2-4/5-1 = -1/2
Since line p is perpendicular to line m, this means that the products of the slopes of p and m must be **–**1:
(slope of p) * (-1/2) = -1
Slope of p = 2
So we must choose the equation that has a slope of 2. If we rewrite the equations in point-slope form (y = mx + b), we see that the equation 2x – y = 3 could be written as y = 2x – 3. This means that the slope of the line 2x – y =3 would be 2, so it could be the equation of line p. The answer is 2x – y = 3.
What line is perpendicular to x + 3_y_ = 6 and travels through point (1,5)?
What line is perpendicular to x + 3_y_ = 6 and travels through point (1,5)?
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Convert the equation to slope intercept form to get y = –1/3_x_ + 2. The old slope is –1/3 and the new slope is 3. Perpendicular slopes must be opposite reciprocals of each other: _m_1 * _m_2 = –1
With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, so b = 2
So y = 3_x_ + 2
Convert the equation to slope intercept form to get y = –1/3_x_ + 2. The old slope is –1/3 and the new slope is 3. Perpendicular slopes must be opposite reciprocals of each other: _m_1 * _m_2 = –1
With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, so b = 2
So y = 3_x_ + 2
Which line below is perpendicular to 
?
Which line below is perpendicular to
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The definition of a perpendicular line is one that has a negative, reciprocal slope to another.
For this particular problem, we must first manipulate our initial equation into a more easily recognizable and useful form: slope-intercept form or 
.
According to our 
formula, our slope for the original line is 
. We are looking for an answer that has a perpendicular slope, or an opposite reciprocal. The opposite reciprocal of 
is 
. Flip the original and multiply it by 
.
Our answer will have a slope of 
. Search the answer choices for 
in the 
position of the 
equation.
is our answer.
(As an aside, the negative reciprocal of 4 is 
. Place the whole number over one and then flip/negate. This does not apply to the above problem, but should be understood to tackle certain permutations of this problem type where the original slope is an integer.)
The definition of a perpendicular line is one that has a negative, reciprocal slope to another.
For this particular problem, we must first manipulate our initial equation into a more easily recognizable and useful form: slope-intercept form or
According to our
Our answer will have a slope of
(As an aside, the negative reciprocal of 4 is
If a line has an equation of 2y=3x+3, what is the slope of a line that is perpendicular to the line?
If a line has an equation of 2y=3x+3, what is the slope of a line that is perpendicular to the line?
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Putting the first equation in slope-intercept form yields y=\frac{3}{2}$x+\frac{3}{2}$.
A perpendicular line has a slope that is the negative inverse. In this case, -$\frac{2}{3}$.
Putting the first equation in slope-intercept form yields y=\frac{3}{2}$x+\frac{3}{2}$.
A perpendicular line has a slope that is the negative inverse. In this case, -$\frac{2}{3}$.
What is the equation for the line that is perpendicular to 
through point 
?
What is the equation for the line that is perpendicular to
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Perpendicular slopes are opposite reciprocals.
The given slope is found by converting the equation to the slope-intercept form.
The slope of the given line is 
and the perpendicular slope is 
.
We can use the given point and the new slope to find the perpendicular equation. Plug in the slope and the given coordinates to solve for the y-intercept.
Using this y-intercept in slope-intercept form, we get out final equation: 
.
Perpendicular slopes are opposite reciprocals.
The given slope is found by converting the equation to the slope-intercept form.
The slope of the given line is
We can use the given point and the new slope to find the perpendicular equation. Plug in the slope and the given coordinates to solve for the y-intercept.
Using this y-intercept in slope-intercept form, we get out final equation:
What line is perpendicular to 
and passes through 
?
What line is perpendicular to
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Convert the given equation to slope-intercept form.
The slope of this line is 
. The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.
The perpendicular slope is 
.
Plug the new slope and the given point into the slope-intercept form to find the y-intercept.
So the equation of the perpendicular line is 
.
Convert the given equation to slope-intercept form.
The slope of this line is
The perpendicular slope is
Plug the new slope and the given point into the slope-intercept form to find the y-intercept.
So the equation of the perpendicular line is
A given line 
is defined by the equation 
. What is the slope of any line that is perpendicular to 
?
A given line
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For a given line 
defined by the equation 
, any line perpendicular to 
must have a slope that is the negative reciprocal of 
's slope 
, 
.
Since in this case 
,
.
For a given line
Since in this case
Given a line 
defined by the equation 
, which of the following lines is perpendicular to 
?
Given a line
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For a given line 
defined by the equation 
, any line perpendicular to 
must have a slope that is the negative reciprocal of 
's slope 
, 
.
In this instance, the slope of line 
is 
, so 
. The only line provided with an equation that has this slope is 
.
For a given line
In this instance, the slope of line
What is the equation of a line that runs perpendicular to the line 2_x_ + y = 5 and passes through the point (2,7)?
What is the equation of a line that runs perpendicular to the line 2_x_ + y = 5 and passes through the point (2,7)?
Tap to see back →
First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2_x_ +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2_x_ + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½_x_ + 6. Rearranged, it is –x/2 + y = 6.
First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2_x_ +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2_x_ + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½_x_ + 6. Rearranged, it is –x/2 + y = 6.
Which of the following equations represents a line that goes through the point and is perpendicular to the line ?
Which of the following equations represents a line that goes through the point
Tap to see back →
In order to solve this problem, we need first to transform the equation from standard form to slope-intercept form:
Transform the original equation to find its slope.
First, subtract from both sides of the equation.
Simplify and rearrange.
Next, divide both sides of the equation by 6.
The slope of our first line is equal to . Perpendicular lines have slopes that are opposite reciprocals of each other; therefore, if the slope of one is x, then the slope of the other is equal to the following:
Let's calculate the opposite reciprocal of our slope:
The slope of our line is equal to 2. We now have the following partial equation:
We are missing the y-intercept, . Substitute the x- and y-values in the given point to solve for the missing y-intercept.
Add 4 to both sides of the equation.
Substitute this value into our partial equation to construct the equation of our line:
In order to solve this problem, we need first to transform the equation from standard form to slope-intercept form:
Transform the original equation to find its slope.
First, subtract
Simplify and rearrange.
Next, divide both sides of the equation by 6.
The slope of our first line is equal to
Let's calculate the opposite reciprocal of our slope:
The slope of our line is equal to 2. We now have the following partial equation:
We are missing the y-intercept,
Add 4 to both sides of the equation.
Substitute this value into our partial equation to construct the equation of our line:
Line m passes through the points (1, 4) and (5, 2). If line p is perpendicular to m, then which of the following could represent the equation for p?
Line m passes through the points (1, 4) and (5, 2). If line p is perpendicular to m, then which of the following could represent the equation for p?
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The slope of m is equal to y2-y1/x2-x1 = 2-4/5-1 = -1/2
Since line p is perpendicular to line m, this means that the products of the slopes of p and m must be **–**1:
(slope of p) * (-1/2) = -1
Slope of p = 2
So we must choose the equation that has a slope of 2. If we rewrite the equations in point-slope form (y = mx + b), we see that the equation 2x – y = 3 could be written as y = 2x – 3. This means that the slope of the line 2x – y =3 would be 2, so it could be the equation of line p. The answer is 2x – y = 3.
The slope of m is equal to y2-y1/x2-x1 = 2-4/5-1 = -1/2
Since line p is perpendicular to line m, this means that the products of the slopes of p and m must be **–**1:
(slope of p) * (-1/2) = -1
Slope of p = 2
So we must choose the equation that has a slope of 2. If we rewrite the equations in point-slope form (y = mx + b), we see that the equation 2x – y = 3 could be written as y = 2x – 3. This means that the slope of the line 2x – y =3 would be 2, so it could be the equation of line p. The answer is 2x – y = 3.
What line is perpendicular to x + 3_y_ = 6 and travels through point (1,5)?
What line is perpendicular to x + 3_y_ = 6 and travels through point (1,5)?
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Convert the equation to slope intercept form to get y = –1/3_x_ + 2. The old slope is –1/3 and the new slope is 3. Perpendicular slopes must be opposite reciprocals of each other: _m_1 * _m_2 = –1
With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, so b = 2
So y = 3_x_ + 2
Convert the equation to slope intercept form to get y = –1/3_x_ + 2. The old slope is –1/3 and the new slope is 3. Perpendicular slopes must be opposite reciprocals of each other: _m_1 * _m_2 = –1
With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, so b = 2
So y = 3_x_ + 2
Which line below is perpendicular to ?
Which line below is perpendicular to
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The definition of a perpendicular line is one that has a negative, reciprocal slope to another.
For this particular problem, we must first manipulate our initial equation into a more easily recognizable and useful form: slope-intercept form or .
According to our formula, our slope for the original line is . We are looking for an answer that has a perpendicular slope, or an opposite reciprocal. The opposite reciprocal of is . Flip the original and multiply it by .
Our answer will have a slope of . Search the answer choices for in the position of the equation.
is our answer.
(As an aside, the negative reciprocal of 4 is . Place the whole number over one and then flip/negate. This does not apply to the above problem, but should be understood to tackle certain permutations of this problem type where the original slope is an integer.)
The definition of a perpendicular line is one that has a negative, reciprocal slope to another.
For this particular problem, we must first manipulate our initial equation into a more easily recognizable and useful form: slope-intercept form or
According to our
Our answer will have a slope of
(As an aside, the negative reciprocal of 4 is
If a line has an equation of 2y=3x+3, what is the slope of a line that is perpendicular to the line?
If a line has an equation of 2y=3x+3, what is the slope of a line that is perpendicular to the line?
Tap to see back →
Putting the first equation in slope-intercept form yields y=\frac{3}{2}$x+\frac{3}{2}$.
A perpendicular line has a slope that is the negative inverse. In this case, -$\frac{2}{3}$.
Putting the first equation in slope-intercept form yields y=\frac{3}{2}$x+\frac{3}{2}$.
A perpendicular line has a slope that is the negative inverse. In this case, -$\frac{2}{3}$.
What is the equation for the line that is perpendicular to through point ?
What is the equation for the line that is perpendicular to
Tap to see back →
Perpendicular slopes are opposite reciprocals.
The given slope is found by converting the equation to the slope-intercept form.
The slope of the given line is and the perpendicular slope is .
We can use the given point and the new slope to find the perpendicular equation. Plug in the slope and the given coordinates to solve for the y-intercept.
Using this y-intercept in slope-intercept form, we get out final equation: .
Perpendicular slopes are opposite reciprocals.
The given slope is found by converting the equation to the slope-intercept form.
The slope of the given line is
We can use the given point and the new slope to find the perpendicular equation. Plug in the slope and the given coordinates to solve for the y-intercept.
Using this y-intercept in slope-intercept form, we get out final equation:
What line is perpendicular to and passes through ?
What line is perpendicular to
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Convert the given equation to slope-intercept form.
The slope of this line is . The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.
The perpendicular slope is .
Plug the new slope and the given point into the slope-intercept form to find the y-intercept.
So the equation of the perpendicular line is .
Convert the given equation to slope-intercept form.
The slope of this line is
The perpendicular slope is
Plug the new slope and the given point into the slope-intercept form to find the y-intercept.
So the equation of the perpendicular line is
A given line is defined by the equation . What is the slope of any line that is perpendicular to ?
A given line
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For a given line defined by the equation , any line perpendicular to must have a slope that is the negative reciprocal of 's slope , .
Since in this case ,
.
For a given line
Since in this case
Given a line defined by the equation , which of the following lines is perpendicular to ?
Given a line
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For a given line defined by the equation , any line perpendicular to must have a slope that is the negative reciprocal of 's slope , .
In this instance, the slope of line is , so . The only line provided with an equation that has this slope is .
For a given line
In this instance, the slope of line