Calculating the slope of a perpendicular line - GMAT Quantitative Reasoning
Card 0 of 6
What is the slope of the line perpendicular to 
?
What is the slope of the line perpendicular to
Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, rewrite the equation in slope intercept form 
:
Slope of given line: 
Negative reciprocal: 
Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, rewrite the equation in slope intercept form
Slope of given line:
Negative reciprocal:
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What is the slope of a line perpendicular to the line of the equation 
?
What is the slope of a line perpendicular to the line of the equation
The graph of 
for any real number 
is a horizontal line. A line parallel to it is a vertical line, which has a slope that is undefined.
The graph of
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Line 1 is the line of the equation 
. Line 2 is perpendicular to this line. What is the slope of Line 2?
Line 1 is the line of the equation
Rewrite in slope-intercept form:
The slope of the line is the coefficient of 
, which is 
. A line perpendicular to this has as its slope the opposite of the reciprocal of 
:
Rewrite in slope-intercept form:
The slope of the line is the coefficient of
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Given:
Calculate the slope of 
, a line perpendicular to 
.
Given:
Calculate the slope of
To find the slope of a line perpendicular to a given line, simply take the opposite reciprocal of the slope of the given line.
Since f(x) is given in slope intercept form,
.
Therefore our original slope is
So our new slope becomes:
To find the slope of a line perpendicular to a given line, simply take the opposite reciprocal of the slope of the given line.
Since f(x) is given in slope intercept form,
Therefore our original slope is
So our new slope becomes:
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What would be the slope of a line perpendicular to the following line?
What would be the slope of a line perpendicular to the following line?
The equation for a line in standard form is written as follows:
Where 
is the slope of the line and 
is the y intercept. By definition, the slope of a line is the negative reciprocal of the slope of the line to which it is perpendicular. So if the given line has a slope of 
, the slope of any line perpendicular to it will have the negative reciprocal of that slope. This gives us:
The equation for a line in standard form is written as follows:
Where
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Give the slope of a line on the coordinate plane.
Statement 1: The line shares an 
-intercept and its 
-intercept with the line of the equation 
.
Statement 2: The line is perpendicular to the line of the equation 
.
Give the slope of a line on the coordinate plane.
Statement 1: The line shares an
Statement 2: The line is perpendicular to the line of the equation
Assume Statement 1 alone. In order to determine the slope of a line on the coordinate plane, the coordinates of two of its points are needed. The 
-intercept of the line of the equation can be found by substituting 
and solving for 
:
The 
-intercept of the line is at the origin, 
. It follows that the 
-intercept is also at the origin. Therefore, Statement 1 only gives one point on the line, and its slope cannot be determined.
Assume Statement 2 alone. The slope of the line of the equation 
can be calculated by putting it in slope-intercept form 
:
The slope of this line is the coefficient of 
, which is 
. A line perpendicular to this one has as its slope the opposite of the reciprocal of 
, which is
.
The question is answered.
Assume Statement 1 alone. In order to determine the slope of a line on the coordinate plane, the coordinates of two of its points are needed. The
The
Assume Statement 2 alone. The slope of the line of the equation
The slope of this line is the coefficient of
The question is answered.
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