Parallel Lines - GMAT Quantitative
Card 1 of 152
What is the equation of the line that is parallel to 
and goes through point 
?
What is the equation of the line that is parallel to
Tap to reveal answer
Parallel lines have the same slope. Therefore, the slope of the new line is 
, as the equation of the original line is 
,with slope 
.
and 
:
Parallel lines have the same slope. Therefore, the slope of the new line is
← Didn't Know|Knew It →
Find the equation of a line that is parallel to 
and passes through the point 
.
Find the equation of a line that is parallel to
Tap to reveal answer
The parallel line has the equation 
. We can find the slope by putting the equation into slope-intercept form, y = mx + b, where m is the slope and b is the intercept. 
becomes 
, so the slope is 2.
We know that our line must have an equation that looks like 
. Now we need the intercept. We can solve for b by plugging in the point (4, 1).
1 = 2(4) + b
b = –7
Then the line in question is 
.
The parallel line has the equation
We know that our line must have an equation that looks like
1 = 2(4) + b
b = –7
Then the line in question is
← Didn't Know|Knew It →
Given:
Which of the following is the equation of a line parallel to 
that has a y-intercept of 
?
Given:
Which of the following is the equation of a line parallel to
Tap to reveal answer
Parallel lines have the same slope, so our slope will still be 4. The y-intercept is just the "+b" at the end. In f(x) the y-intercept is 13. In this case, we need to have a y-intercept of -13, so our equation just becomes:
Parallel lines have the same slope, so our slope will still be 4. The y-intercept is just the "+b" at the end. In f(x) the y-intercept is 13. In this case, we need to have a y-intercept of -13, so our equation just becomes:
← Didn't Know|Knew It →
Find the equation of the line that is parallel to the 
and passes through the point 
.
Find the equation of the line that is parallel to the
Tap to reveal answer
Two lines are parallel if they have the same slope. The slope of g(x) is 6, so eliminate anything without a slope of 6.
Recall slope intercept form which is 
.
We know that the line must have an m of 6 and an (x,y) of (8,9). Plug everything in and go from there.
So we get:
Two lines are parallel if they have the same slope. The slope of g(x) is 6, so eliminate anything without a slope of 6.
Recall slope intercept form which is
We know that the line must have an m of 6 and an (x,y) of (8,9). Plug everything in and go from there.
So we get:
← Didn't Know|Knew It →
Given the function 
, which of the following is the equation of a line parallel to 
and has a 
-intercept of 
?
Given the function
Tap to reveal answer
Given a line 
defined by the equation 
with slope 
, any line that is parallel to 
also has a slope of 
. Since 
, the slope 
is 
and the slope of any line 
parallel to 
also has a slope of 
.
Since 
also needs to have a 
-intercept of 
, then the equation for 
must be 
.
Given a line
Since
← Didn't Know|Knew It →
Given the function 
, which of the following is the equation of a line parallel to 
and has a 
-intercept of 
?
Given the function
Tap to reveal answer
Given a line 
defined by the equation 
with slope 
, any line that is parallel to 
also has a slope of 
. Since 
, the slope 
is 
and the slope of any line 
parallel to 
also has a slope of 
.
Since 
also needs to have a 
-intercept of 
, then the equation for 
must be 
.
Given a line
Since
← Didn't Know|Knew It →
Given the function 
, which of the following is the equation of a line parallel to 
and has a 
-intercept of 
?
Given the function
Tap to reveal answer
Given a line 
defined by the equation 
with slope 
, any line that is parallel to 
also has a slope of 
. Since 
, the slope 
is 
and the slope of any line 
parallel to 
also has a slope of 
.
Since 
also needs to have a 
-intercept of 
, then the equation for 
must be 
.
Given a line
Since
← Didn't Know|Knew It →
What is the slope of the line parallel to 
?
What is the slope of the line parallel to
Tap to reveal answer
Parallel lines have the same slope. Therefore, rewrite the equation in slope intercept form 
:
Parallel lines have the same slope. Therefore, rewrite the equation in slope intercept form
← Didn't Know|Knew It →
Find the slope of any line parallel to the following function.
Find the slope of any line parallel to the following function.
Tap to reveal answer
We need to rearrange this equation to get into 
form.
Begin by adding 6 to both sides to get
Next, divide both sides by 4 to get our slope
So our slope, m, is equal to 3/4. Therefore, any line with the slope 3/4 will be parallel to the original function.
We need to rearrange this equation to get into
Begin by adding 6 to both sides to get
Next, divide both sides by 4 to get our slope
So our slope, m, is equal to 3/4. Therefore, any line with the slope 3/4 will be parallel to the original function.
← Didn't Know|Knew It →
A given line is defined by the equation 
. What is the slope of any line parallel to this line?
A given line is defined by the equation
Tap to reveal answer
Any line that is parallel to a line 
has a slope that is equal to the slope 
. Given 
, 
and therefore any line parallel to the given line must have a slope of 
.
Any line that is parallel to a line
← Didn't Know|Knew It →
A given line is defined by the equation 
. What is the slope of any line parallel to this line?
A given line is defined by the equation
Tap to reveal answer
Any line that is parallel to a line 
has a slope that is equal to the slope 
. Given 
, 
and therefore any line parallel to the given line must have a slope of 
.
Any line that is parallel to a line
← Didn't Know|Knew It →
A given line is defined by the equation 
. What is the slope of any line parallel to this line?
A given line is defined by the equation
Tap to reveal answer
Any line that is parallel to a line 
has a slope that is equal to the slope 
. Given 
, 
and therefore any line parallel to the given line must have a slope of 
.
Any line that is parallel to a line
← 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, 
.
, so the first slope is 
.
, 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 
.
, so the first slope is 
.
, 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.
4.
5.
← Didn't Know|Knew It →
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.
← Didn't Know|Knew It →
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
← Didn't Know|Knew It →
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 →
What is the equation of the line that is parallel to and goes through point ?
What is the equation of the line that is parallel to
Tap to reveal answer
Parallel lines have the same slope. Therefore, the slope of the new line is , as the equation of the original line is ,with slope .
and :
Parallel lines have the same slope. Therefore, the slope of the new line is
← Didn't Know|Knew It →