Calculating whether lines are parallel - GMAT Quantitative
Card 1 of 56
Determine whether 
and 
are parallel lines.
Determine whether
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Parallel lines have the same slope. Therefore, we need to find the slope once both equations are in slope intercept form 
:
The lines are parallel because the slopes are the same.
Parallel lines have the same slope. Therefore, we need to find the slope once both equations are in slope intercept form
The lines are parallel because the slopes are the same.
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Which of the following pairs of lines are parallel?
Which of the following pairs of lines are parallel?
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Two lines are parallel if they have the same slope. Let's go through the answer choices.
1. 
and 
: Both slopes are 3, parallel.
2. 
and 
: Slopes are 2 and 3, not parallel.
3. 
and 
: We need to put these two equations into the form of 
to find the slope, 
.
3x - 2y=5Rightarrow -2y=5-3xRightarrow y=3x/2-5/2, so the first slope is 
.
2x+3y=4Rightarrow 3y=4-2xRightarrow y=-2x/3 + 4/3, so the second slope is 
. These lines are perpendicular, not parallel.
4. 
and 
: Slopes are undefined and 0, respectively, so not parallel.
5. 
and 
: Let's again put these into the form of 
.
5x+4y=1Rightarrow 4y=1-5xRightarrow y=-5x/4 + 1/4, so the first slope is 
.
4x+5y=2Rightarrow 5y=2-4xRightarrow y=-4x/5+2/5, so the second slope is 
. The lines are not parallel.
Two lines are parallel if they have the same slope. Let's go through the answer choices.
1.
2.
3.
3x - 2y=5Rightarrow -2y=5-3xRightarrow y=3x/2-5/2, so the first slope is
2x+3y=4Rightarrow 3y=4-2xRightarrow y=-2x/3 + 4/3, so the second slope is
4.
5.
5x+4y=1Rightarrow 4y=1-5xRightarrow y=-5x/4 + 1/4, so the first slope is
4x+5y=2Rightarrow 5y=2-4xRightarrow y=-4x/5+2/5, so the second slope is
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Three lines - one green, one blue, one red - are drawn on the coordinate axes. They have the following characteristics:
The green line has 
-intercept 
and 
-intercept 
.
The blue line has 
-intercept 
and 
-intercept 
.
The red line has 
-intercept 
and 
-intercept 
.
Which of these lines are parallel to each other?
Three lines - one green, one blue, one red - are drawn on the coordinate axes. They have the following characteristics:
The green line has
The blue line has
The red line has
Which of these lines are parallel to each other?
Tap to reveal answer
Use the intercepts to find the slopes of the lines.
Green: 
Blue: 
Red: 
The blue and red lines have the same slope; the green line has a different slope from the other two. That means only the blue and red lines are parallel.
Use the intercepts to find the slopes of the lines.
Green:
Blue:
Red:
The blue and red lines have the same slope; the green line has a different slope from the other two. That means only the blue and red lines are parallel.
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Which of the following lines is parallel to 
?
Which of the following lines is parallel to
Tap to reveal answer
Two lines are parallel to each other if their slopes have the same value. Since the slope of 
is 
, 
is the only other line provided that has the same slope.
Two lines are parallel to each other if their slopes have the same value. Since the slope of
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Determine whether 
and 
are parallel lines.
Determine whether
Tap to reveal answer
By definition, lines that are parallel to each other must have the same slope. 
has a slope of 
and 
has a slope of 
, therefore they are not parallel because their slopes are not the same.
By definition, lines that are parallel to each other must have the same slope.
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What is the slope of a line that is parallel to 
?
What is the slope of a line that is parallel to
Tap to reveal answer
Two lines are parallel if their slopes have the same value. Since 
has a slope of 
, any line parallel to it must also have a slope of 
.
Two lines are parallel if their slopes have the same value. Since
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Tell whether the lines described by the following are parallel.
g(x) is a linear equation which passes through the points 
and 
.
Tell whether the lines described by the following are parallel.
g(x) is a linear equation which passes through the points
Tap to reveal answer
Tell whether the lines described by the following are parallel.
g(x) is a linear equation which passes through the points 
and 
Begin by recalling that lines are parallel if their slopes are the same and they have different y-intercepts.
Let's find the slope of g(x)
Note that this slope is not the same as f(x), so we do not have parallel lines!
Tell whether the lines described by the following are parallel.
g(x) is a linear equation which passes through the points
Begin by recalling that lines are parallel if their slopes are the same and they have different y-intercepts.
Let's find the slope of g(x)
Note that this slope is not the same as f(x), so we do not have parallel lines!
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Which of the following pairs of lines are parallel?
Which of the following pairs of lines are parallel?
Tap to reveal answer
Two lines are parallel if they have the same slope. Let's go through the answer choices.
1. and : Both slopes are 3, parallel.
2. and : Slopes are 2 and 3, not parallel.
3. and : We need to put these two equations into the form of to find the slope, .
3x - 2y=5Rightarrow -2y=5-3xRightarrow y=3x/2-5/2, so the first slope is .
2x+3y=4Rightarrow 3y=4-2xRightarrow y=-2x/3 + 4/3, so the second slope is . These lines are perpendicular, not parallel.
4. and : Slopes are undefined and 0, respectively, so not parallel.
5. and : Let's again put these into the form of .
5x+4y=1Rightarrow 4y=1-5xRightarrow y=-5x/4 + 1/4, so the first slope is .
4x+5y=2Rightarrow 5y=2-4xRightarrow y=-4x/5+2/5, so the second slope is . The lines are not parallel.
Two lines are parallel if they have the same slope. Let's go through the answer choices.
1.
2.
3.
3x - 2y=5Rightarrow -2y=5-3xRightarrow y=3x/2-5/2, so the first slope is
2x+3y=4Rightarrow 3y=4-2xRightarrow y=-2x/3 + 4/3, so the second slope is
4.
5.
5x+4y=1Rightarrow 4y=1-5xRightarrow y=-5x/4 + 1/4, so the first slope is
4x+5y=2Rightarrow 5y=2-4xRightarrow y=-4x/5+2/5, so the second slope is
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Three lines - one green, one blue, one red - are drawn on the coordinate axes. They have the following characteristics:
The green line has -intercept and -intercept .
The blue line has -intercept and -intercept .
The red line has -intercept and -intercept .
Which of these lines are parallel to each other?
Three lines - one green, one blue, one red - are drawn on the coordinate axes. They have the following characteristics:
The green line has
The blue line has
The red line has
Which of these lines are parallel to each other?
Tap to reveal answer
Use the intercepts to find the slopes of the lines.
Green:
Blue:
Red:
The blue and red lines have the same slope; the green line has a different slope from the other two. That means only the blue and red lines are parallel.
Use the intercepts to find the slopes of the lines.
Green:
Blue:
Red:
The blue and red lines have the same slope; the green line has a different slope from the other two. That means only the blue and red lines are parallel.
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Determine whether and are parallel lines.
Determine whether
Tap to reveal answer
Parallel lines have the same slope. Therefore, we need to find the slope once both equations are in slope intercept form :
The lines are parallel because the slopes are the same.
Parallel lines have the same slope. Therefore, we need to find the slope once both equations are in slope intercept form
The lines are parallel because the slopes are the same.
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Which of the following lines is parallel to ?
Which of the following lines is parallel to
Tap to reveal answer
Two lines are parallel to each other if their slopes have the same value. Since the slope of is , is the only other line provided that has the same slope.
Two lines are parallel to each other if their slopes have the same value. Since the slope of
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Determine whether and are parallel lines.
Determine whether
Tap to reveal answer
By definition, lines that are parallel to each other must have the same slope. has a slope of and has a slope of , therefore they are not parallel because their slopes are not the same.
By definition, lines that are parallel to each other must have the same slope.
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What is the slope of a line that is parallel to ?
What is the slope of a line that is parallel to
Tap to reveal answer
Two lines are parallel if their slopes have the same value. Since has a slope of , any line parallel to it must also have a slope of .
Two lines are parallel if their slopes have the same value. Since
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Tell whether the lines described by the following are parallel.
g(x) is a linear equation which passes through the points and .
Tell whether the lines described by the following are parallel.
g(x) is a linear equation which passes through the points
Tap to reveal answer
Tell whether the lines described by the following are parallel.
g(x) is a linear equation which passes through the points and
Begin by recalling that lines are parallel if their slopes are the same and they have different y-intercepts.
Let's find the slope of g(x)
Note that this slope is not the same as f(x), so we do not have parallel lines!
Tell whether the lines described by the following are parallel.
g(x) is a linear equation which passes through the points
Begin by recalling that lines are parallel if their slopes are the same and they have different y-intercepts.
Let's find the slope of g(x)
Note that this slope is not the same as f(x), so we do not have parallel lines!
← Didn't Know|Knew It →
Determine whether and are parallel lines.
Determine whether
Tap to reveal answer
Parallel lines have the same slope. Therefore, we need to find the slope once both equations are in slope intercept form :
The lines are parallel because the slopes are the same.
Parallel lines have the same slope. Therefore, we need to find the slope once both equations are in slope intercept form
The lines are parallel because the slopes are the same.
← Didn't Know|Knew It →
Which of the following pairs of lines are parallel?
Which of the following pairs of lines are parallel?
Tap to reveal answer
Two lines are parallel if they have the same slope. Let's go through the answer choices.
1. and : Both slopes are 3, parallel.
2. and : Slopes are 2 and 3, not parallel.
3. and : We need to put these two equations into the form of to find the slope, .
3x - 2y=5Rightarrow -2y=5-3xRightarrow y=3x/2-5/2, so the first slope is .
2x+3y=4Rightarrow 3y=4-2xRightarrow y=-2x/3 + 4/3, so the second slope is . These lines are perpendicular, not parallel.
4. and : Slopes are undefined and 0, respectively, so not parallel.
5. and : Let's again put these into the form of .
5x+4y=1Rightarrow 4y=1-5xRightarrow y=-5x/4 + 1/4, so the first slope is .
4x+5y=2Rightarrow 5y=2-4xRightarrow y=-4x/5+2/5, so the second slope is . The lines are not parallel.
Two lines are parallel if they have the same slope. Let's go through the answer choices.
1.
2.
3.
3x - 2y=5Rightarrow -2y=5-3xRightarrow y=3x/2-5/2, so the first slope is
2x+3y=4Rightarrow 3y=4-2xRightarrow y=-2x/3 + 4/3, so the second slope is
4.
5.
5x+4y=1Rightarrow 4y=1-5xRightarrow y=-5x/4 + 1/4, so the first slope is
4x+5y=2Rightarrow 5y=2-4xRightarrow y=-4x/5+2/5, so the second slope is
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Three lines - one green, one blue, one red - are drawn on the coordinate axes. They have the following characteristics:
The green line has -intercept and -intercept .
The blue line has -intercept and -intercept .
The red line has -intercept and -intercept .
Which of these lines are parallel to each other?
Three lines - one green, one blue, one red - are drawn on the coordinate axes. They have the following characteristics:
The green line has
The blue line has
The red line has
Which of these lines are parallel to each other?
Tap to reveal answer
Use the intercepts to find the slopes of the lines.
Green:
Blue:
Red:
The blue and red lines have the same slope; the green line has a different slope from the other two. That means only the blue and red lines are parallel.
Use the intercepts to find the slopes of the lines.
Green:
Blue:
Red:
The blue and red lines have the same slope; the green line has a different slope from the other two. That means only the blue and red lines are parallel.
← Didn't Know|Knew It →
Which of the following lines is parallel to ?
Which of the following lines is parallel to
Tap to reveal answer
Two lines are parallel to each other if their slopes have the same value. Since the slope of is , is the only other line provided that has the same slope.
Two lines are parallel to each other if their slopes have the same value. Since the slope of
← Didn't Know|Knew It →
Determine whether and are parallel lines.
Determine whether
Tap to reveal answer
By definition, lines that are parallel to each other must have the same slope. has a slope of and has a slope of , therefore they are not parallel because their slopes are not the same.
By definition, lines that are parallel to each other must have the same slope.
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What is the slope of a line that is parallel to ?
What is the slope of a line that is parallel to
Tap to reveal answer
Two lines are parallel if their slopes have the same value. Since has a slope of , any line parallel to it must also have a slope of .
Two lines are parallel if their slopes have the same value. Since
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