How to find out if lines are perpendicular - ACT Math
Card 0 of 9
Which of the following lines is perpendicular to the line 
?
Which of the following lines is perpendicular to the line
Perpendicular lines will have slopes that are negative reciprocals of one another. Our first step will be to find the slope of the given line by putting the equation into slope-intercept form.
The slope of this line is 
. The negative reciprocal will be 
, which will be the slope of the perpendicular line.
Now we need to find the answer choice with this slope by converting to slope-intercept form.
This equation has a slope of 
, and must be our answer.
Perpendicular lines will have slopes that are negative reciprocals of one another. Our first step will be to find the slope of the given line by putting the equation into slope-intercept form.
The slope of this line is
Now we need to find the answer choice with this slope by converting to slope-intercept form.
This equation has a slope of
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Which of the following equations represents a line that is perpendicular to the line with points 
and 
?
Which of the following equations represents a line that is perpendicular to the line with points
If lines are perpendicular, then their slopes will be negative reciprocals.
First, we need to find the slope of the given line.
Because we know that our given line's slope is 
, the slope of the line perpendicular to it must be 
.
If lines are perpendicular, then their slopes will be negative reciprocals.
First, we need to find the slope of the given line.
Because we know that our given line's slope is
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Which of the following lines is perpindicular to 
Which of the following lines is perpindicular to
When determining if a two lines are perpindicular, we are only concerned about their slopes. Consider the basic equation of a line, 
, where m is the slope of the line. Two lines are perpindicular to each other if one slope is the negative and reciprocal of the other.
The first step of this problem is to get it into the form, 
, which is 
. Now we know that the slope, m, is 
. The reciprocal of that is 
, and the negative of that is 
. Therefore, any line that has a slope of 
will be perpindicular to the original line.
When determining if a two lines are perpindicular, we are only concerned about their slopes. Consider the basic equation of a line,
The first step of this problem is to get it into the form,
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Which of the following lines is perpendicular to the line with the given equation:
?
Which of the following lines is perpendicular to the line with the given equation:
First we must recognize that the equation is given in slope-intercept form, 
where 
is the slope of the line.
Two lines are perpendicular if and only if the product of their slopes is 
. In other words, the slope of a line that is perpendicular to a given line is the negative reciprocal of that slope.
Thus, for a line with a given slope of 3, the line perpendicular to that slope must be the negative reciprocal of 3, or 
.
To double check that that does indeed give a product of 
when multiplied by three simply compute the product:
First we must recognize that the equation is given in slope-intercept form,
Two lines are perpendicular if and only if the product of their slopes is
Thus, for a line with a given slope of 3, the line perpendicular to that slope must be the negative reciprocal of 3, or
To double check that that does indeed give a product of
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Are the following two lines parallel, perpendicular, or neither:
and 
Are the following two lines parallel, perpendicular, or neither:
Perpendicular lines have slopes whose product is 
.
The slope is controlled by the coefficient, 
from the genral form of the slope-intercept equation:
Thus the two lines are perpendicular because:
has 
and
has 
which when multiplied together results in,
.
Perpendicular lines have slopes whose product is
The slope is controlled by the coefficient,
Thus the two lines are perpendicular because:
and
which when multiplied together results in,
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Are the following two lines perpendicular:
Are the following two lines perpendicular:
For two lines to be perpendicular, their slopes have to have a product of 
. Find the slopes by the coefficient in front of the 
.
and so the two lines are perpendicular. The y-intercept does not matter for determine perpendicularity.
For two lines to be perpendicular, their slopes have to have a product of
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Are the following two lines perpendicular:
and
Are the following two lines perpendicular:
For two lines to be perpendicular they have to have slopes that multiply to get 
. The slope is found from the 
in the general equation: 
.
For the first line, 
and for the second 
. 
and so the lines are not perpendicular.
For two lines to be perpendicular they have to have slopes that multiply to get
For the first line,
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Are the lines described by the equations 
and 
perpendicular to one another? Why or why not?
Are the lines described by the equations
If the slopes of two lines can be calculated, an easy way to determine whether they are perpendicular is to multiply their slopes. If the product of the slopes is 
, then the lines are perpendicular.
In this case, the slope of the line 
is 
and the slope of the line 
is 
.
Since 
, the slopes are not perpendicular.
If the slopes of two lines can be calculated, an easy way to determine whether they are perpendicular is to multiply their slopes. If the product of the slopes is
In this case, the slope of the line
Since
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Line 
, which follows the equation 
, intersects line 
at 
. If line 
also passes through 
, are 
and 
perpendicular?
Line
The product of perpendicular slopes is always 
. Knowing this, and seeing that the slope of line 
is 
, we know any perpendicular line will have a slope of 
.
Since line 
passes through 
and 
, we can use the slope equation:
Since the two slopes' product is 
, the lines are perpendicular.
The product of perpendicular slopes is always
Since line
Since the two slopes' product is
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