How to find the equation of a perpendicular line - GRE Quantitative Reasoning
Card 1 of 40
Which of the following is a line perpendicular to the line passing through 
and 
?
Which of the following is a line perpendicular to the line passing through
Tap to reveal answer
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of 
. The only possible option is, therefore, 
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of
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Which of the following equations represents a line perpendicular to 3x + 4y = 5?
Which of the following equations represents a line perpendicular to 3x + 4y = 5?
Tap to reveal answer
Perpendicular lines have opposite and reciprocal slopes. Therefore, let us find the slope of our line and appropriately modify it to find the perpendicular line. To find the slope of our line, remember that in the slope-intercept form (y = mx + b), m represents the slope.
3x + 4y = 5 => 4y = 5 - 3x => y = (-3/4)x + 5/4
Therefore, the slope of our line is -3/4. The perpendicular to this would be 4 / 3. Therefore, only y = (4/3)x - 15 is perpendicular.
Perpendicular lines have opposite and reciprocal slopes. Therefore, let us find the slope of our line and appropriately modify it to find the perpendicular line. To find the slope of our line, remember that in the slope-intercept form (y = mx + b), m represents the slope.
3x + 4y = 5 => 4y = 5 - 3x => y = (-3/4)x + 5/4
Therefore, the slope of our line is -3/4. The perpendicular to this would be 4 / 3. Therefore, only y = (4/3)x - 15 is perpendicular.
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What is the equation for the line passing through the point (5,4) and is perpendicular to the line 8y + 4x = 10?
What is the equation for the line passing through the point (5,4) and is perpendicular to the line 8y + 4x = 10?
Tap to reveal answer
To solve this, we need to use the point-slope form. However, to do this, we need to ascertain the slope of the perpendicular line. For this, get 8y + 4x = 10 into slope-intercept form:
8y = -4x + 10; y = (-1/2)x + 1.25
Therefore, the slope of this line is -1/2 and its perpendicular (opposite and reciprocal) slope is 2.
The point slope form is: (y – y1) = m * (x – x1)
For our data it is: y – 4 = 2 * (x – 5)
Simplifying, we get: y – 4 = 2 x – 10; y = 2x – 6
To solve this, we need to use the point-slope form. However, to do this, we need to ascertain the slope of the perpendicular line. For this, get 8y + 4x = 10 into slope-intercept form:
8y = -4x + 10; y = (-1/2)x + 1.25
Therefore, the slope of this line is -1/2 and its perpendicular (opposite and reciprocal) slope is 2.
The point slope form is: (y – y1) = m * (x – x1)
For our data it is: y – 4 = 2 * (x – 5)
Simplifying, we get: y – 4 = 2 x – 10; y = 2x – 6
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Which of the following is an equation of a line that is perpendicular to 
?
Which of the following is an equation of a line that is perpendicular to
Tap to reveal answer
Rewrite the equation in 
form.
The perpendicular line will have a slope which is the negative reciprocal of the slope 
.
Rewrite the equation in
The perpendicular line will have a slope which is the negative reciprocal of the slope
← Didn't Know|Knew It →
Which of the following is a line perpendicular to the line passing through 
and 
?
Which of the following is a line perpendicular to the line passing through
Tap to reveal answer
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of 
. The only possible option is, therefore, 
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of
← Didn't Know|Knew It →
Which of the following is a line perpendicular to the line passing through and ?
Which of the following is a line perpendicular to the line passing through
Tap to reveal answer
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of . The only possible option is, therefore,
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of
← Didn't Know|Knew It →
Which of the following equations represents a line perpendicular to 3x + 4y = 5?
Which of the following equations represents a line perpendicular to 3x + 4y = 5?
Tap to reveal answer
Perpendicular lines have opposite and reciprocal slopes. Therefore, let us find the slope of our line and appropriately modify it to find the perpendicular line. To find the slope of our line, remember that in the slope-intercept form (y = mx + b), m represents the slope.
3x + 4y = 5 => 4y = 5 - 3x => y = (-3/4)x + 5/4
Therefore, the slope of our line is -3/4. The perpendicular to this would be 4 / 3. Therefore, only y = (4/3)x - 15 is perpendicular.
Perpendicular lines have opposite and reciprocal slopes. Therefore, let us find the slope of our line and appropriately modify it to find the perpendicular line. To find the slope of our line, remember that in the slope-intercept form (y = mx + b), m represents the slope.
3x + 4y = 5 => 4y = 5 - 3x => y = (-3/4)x + 5/4
Therefore, the slope of our line is -3/4. The perpendicular to this would be 4 / 3. Therefore, only y = (4/3)x - 15 is perpendicular.
← Didn't Know|Knew It →
What is the equation for the line passing through the point (5,4) and is perpendicular to the line 8y + 4x = 10?
What is the equation for the line passing through the point (5,4) and is perpendicular to the line 8y + 4x = 10?
Tap to reveal answer
To solve this, we need to use the point-slope form. However, to do this, we need to ascertain the slope of the perpendicular line. For this, get 8y + 4x = 10 into slope-intercept form:
8y = -4x + 10; y = (-1/2)x + 1.25
Therefore, the slope of this line is -1/2 and its perpendicular (opposite and reciprocal) slope is 2.
The point slope form is: (y – y1) = m * (x – x1)
For our data it is: y – 4 = 2 * (x – 5)
Simplifying, we get: y – 4 = 2 x – 10; y = 2x – 6
To solve this, we need to use the point-slope form. However, to do this, we need to ascertain the slope of the perpendicular line. For this, get 8y + 4x = 10 into slope-intercept form:
8y = -4x + 10; y = (-1/2)x + 1.25
Therefore, the slope of this line is -1/2 and its perpendicular (opposite and reciprocal) slope is 2.
The point slope form is: (y – y1) = m * (x – x1)
For our data it is: y – 4 = 2 * (x – 5)
Simplifying, we get: y – 4 = 2 x – 10; y = 2x – 6
← Didn't Know|Knew It →
Which of the following is an equation of a line that is perpendicular to ?
Which of the following is an equation of a line that is perpendicular to
Tap to reveal answer
Rewrite the equation in form.
The perpendicular line will have a slope which is the negative reciprocal of the slope .
Rewrite the equation in
The perpendicular line will have a slope which is the negative reciprocal of the slope
← Didn't Know|Knew It →
Which of the following is a line perpendicular to the line passing through and ?
Which of the following is a line perpendicular to the line passing through
Tap to reveal answer
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of . The only possible option is, therefore,
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of
← Didn't Know|Knew It →
Which of the following is a line perpendicular to the line passing through and ?
Which of the following is a line perpendicular to the line passing through
Tap to reveal answer
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of . The only possible option is, therefore,
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of
← Didn't Know|Knew It →
Which of the following equations represents a line perpendicular to 3x + 4y = 5?
Which of the following equations represents a line perpendicular to 3x + 4y = 5?
Tap to reveal answer
Perpendicular lines have opposite and reciprocal slopes. Therefore, let us find the slope of our line and appropriately modify it to find the perpendicular line. To find the slope of our line, remember that in the slope-intercept form (y = mx + b), m represents the slope.
3x + 4y = 5 => 4y = 5 - 3x => y = (-3/4)x + 5/4
Therefore, the slope of our line is -3/4. The perpendicular to this would be 4 / 3. Therefore, only y = (4/3)x - 15 is perpendicular.
Perpendicular lines have opposite and reciprocal slopes. Therefore, let us find the slope of our line and appropriately modify it to find the perpendicular line. To find the slope of our line, remember that in the slope-intercept form (y = mx + b), m represents the slope.
3x + 4y = 5 => 4y = 5 - 3x => y = (-3/4)x + 5/4
Therefore, the slope of our line is -3/4. The perpendicular to this would be 4 / 3. Therefore, only y = (4/3)x - 15 is perpendicular.
← Didn't Know|Knew It →
What is the equation for the line passing through the point (5,4) and is perpendicular to the line 8y + 4x = 10?
What is the equation for the line passing through the point (5,4) and is perpendicular to the line 8y + 4x = 10?
Tap to reveal answer
To solve this, we need to use the point-slope form. However, to do this, we need to ascertain the slope of the perpendicular line. For this, get 8y + 4x = 10 into slope-intercept form:
8y = -4x + 10; y = (-1/2)x + 1.25
Therefore, the slope of this line is -1/2 and its perpendicular (opposite and reciprocal) slope is 2.
The point slope form is: (y – y1) = m * (x – x1)
For our data it is: y – 4 = 2 * (x – 5)
Simplifying, we get: y – 4 = 2 x – 10; y = 2x – 6
To solve this, we need to use the point-slope form. However, to do this, we need to ascertain the slope of the perpendicular line. For this, get 8y + 4x = 10 into slope-intercept form:
8y = -4x + 10; y = (-1/2)x + 1.25
Therefore, the slope of this line is -1/2 and its perpendicular (opposite and reciprocal) slope is 2.
The point slope form is: (y – y1) = m * (x – x1)
For our data it is: y – 4 = 2 * (x – 5)
Simplifying, we get: y – 4 = 2 x – 10; y = 2x – 6
← Didn't Know|Knew It →
Which of the following is an equation of a line that is perpendicular to ?
Which of the following is an equation of a line that is perpendicular to
Tap to reveal answer
Rewrite the equation in form.
The perpendicular line will have a slope which is the negative reciprocal of the slope .
Rewrite the equation in
The perpendicular line will have a slope which is the negative reciprocal of the slope
← Didn't Know|Knew It →
Which of the following is a line perpendicular to the line passing through and ?
Which of the following is a line perpendicular to the line passing through
Tap to reveal answer
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of . The only possible option is, therefore,
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of
← Didn't Know|Knew It →
Which of the following is a line perpendicular to the line passing through and ?
Which of the following is a line perpendicular to the line passing through
Tap to reveal answer
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of . The only possible option is, therefore,
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of
← Didn't Know|Knew It →
Which of the following equations represents a line perpendicular to 3x + 4y = 5?
Which of the following equations represents a line perpendicular to 3x + 4y = 5?
Tap to reveal answer
Perpendicular lines have opposite and reciprocal slopes. Therefore, let us find the slope of our line and appropriately modify it to find the perpendicular line. To find the slope of our line, remember that in the slope-intercept form (y = mx + b), m represents the slope.
3x + 4y = 5 => 4y = 5 - 3x => y = (-3/4)x + 5/4
Therefore, the slope of our line is -3/4. The perpendicular to this would be 4 / 3. Therefore, only y = (4/3)x - 15 is perpendicular.
Perpendicular lines have opposite and reciprocal slopes. Therefore, let us find the slope of our line and appropriately modify it to find the perpendicular line. To find the slope of our line, remember that in the slope-intercept form (y = mx + b), m represents the slope.
3x + 4y = 5 => 4y = 5 - 3x => y = (-3/4)x + 5/4
Therefore, the slope of our line is -3/4. The perpendicular to this would be 4 / 3. Therefore, only y = (4/3)x - 15 is perpendicular.
← Didn't Know|Knew It →
What is the equation for the line passing through the point (5,4) and is perpendicular to the line 8y + 4x = 10?
What is the equation for the line passing through the point (5,4) and is perpendicular to the line 8y + 4x = 10?
Tap to reveal answer
To solve this, we need to use the point-slope form. However, to do this, we need to ascertain the slope of the perpendicular line. For this, get 8y + 4x = 10 into slope-intercept form:
8y = -4x + 10; y = (-1/2)x + 1.25
Therefore, the slope of this line is -1/2 and its perpendicular (opposite and reciprocal) slope is 2.
The point slope form is: (y – y1) = m * (x – x1)
For our data it is: y – 4 = 2 * (x – 5)
Simplifying, we get: y – 4 = 2 x – 10; y = 2x – 6
To solve this, we need to use the point-slope form. However, to do this, we need to ascertain the slope of the perpendicular line. For this, get 8y + 4x = 10 into slope-intercept form:
8y = -4x + 10; y = (-1/2)x + 1.25
Therefore, the slope of this line is -1/2 and its perpendicular (opposite and reciprocal) slope is 2.
The point slope form is: (y – y1) = m * (x – x1)
For our data it is: y – 4 = 2 * (x – 5)
Simplifying, we get: y – 4 = 2 x – 10; y = 2x – 6
← Didn't Know|Knew It →
Which of the following is an equation of a line that is perpendicular to ?
Which of the following is an equation of a line that is perpendicular to
Tap to reveal answer
Rewrite the equation in form.
The perpendicular line will have a slope which is the negative reciprocal of the slope .
Rewrite the equation in
The perpendicular line will have a slope which is the negative reciprocal of the slope
← Didn't Know|Knew It →
Which of the following is a line perpendicular to the line passing through and ?
Which of the following is a line perpendicular to the line passing through
Tap to reveal answer
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of . The only possible option is, therefore,
To find if something is perpendicular, you need to first know the slope of your given line. Based on your points, this is easy. Recall that slope is merely:
This is:
Since a perpendicular line has a slope that is both opposite in sign and reciprocal, you need to choose a line with a slope of
← Didn't Know|Knew It →