All GMAT Math Resources
Example Questions
Example Question #1 : Parallel Lines
Which of the following pairs of lines are parallel?
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.
Example Question #2 : Parallel Lines
Determine whether and are parallel lines.
No, because the slopes are not similar.
No, because the slopes are not negative reciprocals of each other.
Yes, because the slopes are the same.
Yes, because the slopes are negative reciprocals of each other.
Yes, 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.
Example Question #2 : Parallel Lines
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?
Only the green line and the red line are parallel to each other.
All three lines are parallel to one another.
Only the blue line and the red line are parallel to each other.
Only the blue line and the green line are parallel to each other.
No two of these lines are parallel to each other.
Only the blue line and the red line are parallel to each other.
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.
Example Question #2 : Calculating Whether Lines Are Parallel
What is the slope of a line that is parallel to ?
None of the above
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 .
Example Question #3 : Calculating Whether Lines Are Parallel
Which of the following lines is parallel to ?
Two of the answers provided are correct.
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.
Example Question #3 : Parallel Lines
Determine whether and are parallel lines.
Yes, because the slopes are the same.
Cannot determine.
No, because the slopes are not negative reciprocals of each other.
Yes, because the slopes are negative reciprocals of each other.
No, because the slopes are not the same.
No, because the slopes are not the same.
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.
Example Question #36 : Coordinate Geometry
Tell whether the lines described by the following are parallel.
g(x) is a linear equation which passes through the points and .
They are parallel, because their slopes are opposite reciprocals of each other.
There are not parallel, they are the same line.
They are not parallel, because they have different slopes.
They are parallel, because they have the same slope.
They are not parallel, because they have different slopes.
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!
Example Question #1 : Calculating The Slope Of Parallel Lines
What is the slope of the line parallel to ?
Parallel lines have the same slope. Therefore, rewrite the equation in slope intercept form :
Example Question #6 : Parallel Lines
Find the slope of any line parallel to the following function.
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.
Example Question #1 : Calculating The Slope Of Parallel Lines
A given line is defined by the equation . What is the slope of any line parallel to this line?
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 .