DSQ: Calculating the slope of parallel lines - GMAT Quantitative
Card 0 of 28
Consider this system of equations:
Does this system has exactly one solution?
Statement 1: The lines representing the equations are parallel.
Statement 2: 
Consider this system of equations:
Does this system has exactly one solution?
Statement 1: The lines representing the equations are parallel.
Statement 2:
Tap to see back →
The solution of a system of linear equations is the point at which their lines intersect; if they are parallel, then by definition, there is no such point, and the system has no solution.
If 
, then we can rewrite the second equation as
In slope-intercept form:
This line has a slope of 
. The other equation has a line with slope of 
also, as can be easily seen since it is already in slope-intercept form. Since both equations have lines with the same slope, they are either the same line or parallel lines; either way, the system does not have exactly one solution.
The solution of a system of linear equations is the point at which their lines intersect; if they are parallel, then by definition, there is no such point, and the system has no solution.
If
In slope-intercept form:
This line has a slope of
If 
is modeled by 
, find the slope of 
.
I) 
.
II) 
crosses the 
-axis at 
.
If
I)
II)
Tap to see back →
I) Tells us the two lines are parallel. Parallel lines have the same slope.
II) Gives us the x-intercept of b(t). By itself this gives us no clue as to the slop of b. If we had another point on b(t) we could find the slope, but we don't have another point.
So, statement I is what we need.
I) Tells us the two lines are parallel. Parallel lines have the same slope.
II) Gives us the x-intercept of b(t). By itself this gives us no clue as to the slop of b. If we had another point on b(t) we could find the slope, but we don't have another point.
So, statement I is what we need.
Calculate the slope of a line parallel to line 
.
- Line
passes through points 
and 
.
- The equation for line
is 
.
Calculate the slope of a line parallel to line
- Line
- The equation for line
Tap to see back →
Statement 1: Since we're referring to a line parallel to line XY, the slopes will be identical. We can use the points provided to calculate the slope:
We can simplify the slope to just 
.
Statement 2: Finding the slope of a line parallel to line XY is really straightforward when given the equation of a line.
Where 
is the slope and 
the y-intercept.
In this case, our 
value is 
.\
Each statement alone is sufficient to answer the question.
Statement 1: Since we're referring to a line parallel to line XY, the slopes will be identical. We can use the points provided to calculate the slope:
We can simplify the slope to just
Statement 2: Finding the slope of a line parallel to line XY is really straightforward when given the equation of a line.
Where
In this case, our
Each statement alone is sufficient to answer the question.
Find the slope of the line parallel to 
.
I) 
passes through the point 
.
II) 
has an x-intercept of 290.
Find the slope of the line parallel to
I)
II)
Tap to see back →
Recall that parallel lines have the same slope and that slope can be calculated from any two points.
Statement I gives us a point on 
Statement II gives us the x-intercept, a.k.a. the point 
.
Therfore, using both statements, we can find the slope of 
and any line parallel to it.
Recall that parallel lines have the same slope and that slope can be calculated from any two points.
Statement I gives us a point on
Statement II gives us the x-intercept, a.k.a. the point
Therfore, using both statements, we can find the slope of
Consider this system of equations:
Does this system has exactly one solution?
Statement 1: The lines representing the equations are parallel.
Statement 2:
Consider this system of equations:
Does this system has exactly one solution?
Statement 1: The lines representing the equations are parallel.
Statement 2:
Tap to see back →
The solution of a system of linear equations is the point at which their lines intersect; if they are parallel, then by definition, there is no such point, and the system has no solution.
If , then we can rewrite the second equation as
In slope-intercept form:
This line has a slope of . The other equation has a line with slope of also, as can be easily seen since it is already in slope-intercept form. Since both equations have lines with the same slope, they are either the same line or parallel lines; either way, the system does not have exactly one solution.
The solution of a system of linear equations is the point at which their lines intersect; if they are parallel, then by definition, there is no such point, and the system has no solution.
If
In slope-intercept form:
This line has a slope of
If is modeled by , find the slope of .
I) .
II) crosses the -axis at .
If
I)
II)
Tap to see back →
I) Tells us the two lines are parallel. Parallel lines have the same slope.
II) Gives us the x-intercept of b(t). By itself this gives us no clue as to the slop of b. If we had another point on b(t) we could find the slope, but we don't have another point.
So, statement I is what we need.
I) Tells us the two lines are parallel. Parallel lines have the same slope.
II) Gives us the x-intercept of b(t). By itself this gives us no clue as to the slop of b. If we had another point on b(t) we could find the slope, but we don't have another point.
So, statement I is what we need.
Calculate the slope of a line parallel to line .
- Line passes through points and .
- The equation for line is .
Calculate the slope of a line parallel to line
- Line
- The equation for line
Tap to see back →
Statement 1: Since we're referring to a line parallel to line XY, the slopes will be identical. We can use the points provided to calculate the slope:
We can simplify the slope to just .
Statement 2: Finding the slope of a line parallel to line XY is really straightforward when given the equation of a line.
Where is the slope and the y-intercept.
In this case, our value is .\
Each statement alone is sufficient to answer the question.
Statement 1: Since we're referring to a line parallel to line XY, the slopes will be identical. We can use the points provided to calculate the slope:
We can simplify the slope to just
Statement 2: Finding the slope of a line parallel to line XY is really straightforward when given the equation of a line.
Where
In this case, our
Each statement alone is sufficient to answer the question.
Find the slope of the line parallel to .
I) passes through the point .
II) has an x-intercept of 290.
Find the slope of the line parallel to
I)
II)
Tap to see back →
Recall that parallel lines have the same slope and that slope can be calculated from any two points.
Statement I gives us a point on
Statement II gives us the x-intercept, a.k.a. the point .
Therfore, using both statements, we can find the slope of and any line parallel to it.
Recall that parallel lines have the same slope and that slope can be calculated from any two points.
Statement I gives us a point on
Statement II gives us the x-intercept, a.k.a. the point
Therfore, using both statements, we can find the slope of
Consider this system of equations:
Does this system has exactly one solution?
Statement 1: The lines representing the equations are parallel.
Statement 2:
Consider this system of equations:
Does this system has exactly one solution?
Statement 1: The lines representing the equations are parallel.
Statement 2:
Tap to see back →
The solution of a system of linear equations is the point at which their lines intersect; if they are parallel, then by definition, there is no such point, and the system has no solution.
If , then we can rewrite the second equation as
In slope-intercept form:
This line has a slope of . The other equation has a line with slope of also, as can be easily seen since it is already in slope-intercept form. Since both equations have lines with the same slope, they are either the same line or parallel lines; either way, the system does not have exactly one solution.
The solution of a system of linear equations is the point at which their lines intersect; if they are parallel, then by definition, there is no such point, and the system has no solution.
If
In slope-intercept form:
This line has a slope of
If is modeled by , find the slope of .
I) .
II) crosses the -axis at .
If
I)
II)
Tap to see back →
I) Tells us the two lines are parallel. Parallel lines have the same slope.
II) Gives us the x-intercept of b(t). By itself this gives us no clue as to the slop of b. If we had another point on b(t) we could find the slope, but we don't have another point.
So, statement I is what we need.
I) Tells us the two lines are parallel. Parallel lines have the same slope.
II) Gives us the x-intercept of b(t). By itself this gives us no clue as to the slop of b. If we had another point on b(t) we could find the slope, but we don't have another point.
So, statement I is what we need.
Calculate the slope of a line parallel to line .
- Line passes through points and .
- The equation for line is .
Calculate the slope of a line parallel to line
- Line
- The equation for line
Tap to see back →
Statement 1: Since we're referring to a line parallel to line XY, the slopes will be identical. We can use the points provided to calculate the slope:
We can simplify the slope to just .
Statement 2: Finding the slope of a line parallel to line XY is really straightforward when given the equation of a line.
Where is the slope and the y-intercept.
In this case, our value is .\
Each statement alone is sufficient to answer the question.
Statement 1: Since we're referring to a line parallel to line XY, the slopes will be identical. We can use the points provided to calculate the slope:
We can simplify the slope to just
Statement 2: Finding the slope of a line parallel to line XY is really straightforward when given the equation of a line.
Where
In this case, our
Each statement alone is sufficient to answer the question.
Find the slope of the line parallel to .
I) passes through the point .
II) has an x-intercept of 290.
Find the slope of the line parallel to
I)
II)
Tap to see back →
Recall that parallel lines have the same slope and that slope can be calculated from any two points.
Statement I gives us a point on
Statement II gives us the x-intercept, a.k.a. the point .
Therfore, using both statements, we can find the slope of and any line parallel to it.
Recall that parallel lines have the same slope and that slope can be calculated from any two points.
Statement I gives us a point on
Statement II gives us the x-intercept, a.k.a. the point
Therfore, using both statements, we can find the slope of
Consider this system of equations:
Does this system has exactly one solution?
Statement 1: The lines representing the equations are parallel.
Statement 2:
Consider this system of equations:
Does this system has exactly one solution?
Statement 1: The lines representing the equations are parallel.
Statement 2:
Tap to see back →
The solution of a system of linear equations is the point at which their lines intersect; if they are parallel, then by definition, there is no such point, and the system has no solution.
If , then we can rewrite the second equation as
In slope-intercept form:
This line has a slope of . The other equation has a line with slope of also, as can be easily seen since it is already in slope-intercept form. Since both equations have lines with the same slope, they are either the same line or parallel lines; either way, the system does not have exactly one solution.
The solution of a system of linear equations is the point at which their lines intersect; if they are parallel, then by definition, there is no such point, and the system has no solution.
If
In slope-intercept form:
This line has a slope of
If is modeled by , find the slope of .
I) .
II) crosses the -axis at .
If
I)
II)
Tap to see back →
I) Tells us the two lines are parallel. Parallel lines have the same slope.
II) Gives us the x-intercept of b(t). By itself this gives us no clue as to the slop of b. If we had another point on b(t) we could find the slope, but we don't have another point.
So, statement I is what we need.
I) Tells us the two lines are parallel. Parallel lines have the same slope.
II) Gives us the x-intercept of b(t). By itself this gives us no clue as to the slop of b. If we had another point on b(t) we could find the slope, but we don't have another point.
So, statement I is what we need.
Calculate the slope of a line parallel to line .
- Line passes through points and .
- The equation for line is .
Calculate the slope of a line parallel to line
- Line
- The equation for line
Tap to see back →
Statement 1: Since we're referring to a line parallel to line XY, the slopes will be identical. We can use the points provided to calculate the slope:
We can simplify the slope to just .
Statement 2: Finding the slope of a line parallel to line XY is really straightforward when given the equation of a line.
Where is the slope and the y-intercept.
In this case, our value is .\
Each statement alone is sufficient to answer the question.
Statement 1: Since we're referring to a line parallel to line XY, the slopes will be identical. We can use the points provided to calculate the slope:
We can simplify the slope to just
Statement 2: Finding the slope of a line parallel to line XY is really straightforward when given the equation of a line.
Where
In this case, our
Each statement alone is sufficient to answer the question.
Find the slope of the line parallel to .
I) passes through the point .
II) has an x-intercept of 290.
Find the slope of the line parallel to
I)
II)
Tap to see back →
Recall that parallel lines have the same slope and that slope can be calculated from any two points.
Statement I gives us a point on
Statement II gives us the x-intercept, a.k.a. the point .
Therfore, using both statements, we can find the slope of and any line parallel to it.
Recall that parallel lines have the same slope and that slope can be calculated from any two points.
Statement I gives us a point on
Statement II gives us the x-intercept, a.k.a. the point
Therfore, using both statements, we can find the slope of
Consider this system of equations:
Does this system has exactly one solution?
Statement 1: The lines representing the equations are parallel.
Statement 2:
Consider this system of equations:
Does this system has exactly one solution?
Statement 1: The lines representing the equations are parallel.
Statement 2:
Tap to see back →
The solution of a system of linear equations is the point at which their lines intersect; if they are parallel, then by definition, there is no such point, and the system has no solution.
If , then we can rewrite the second equation as
In slope-intercept form:
This line has a slope of . The other equation has a line with slope of also, as can be easily seen since it is already in slope-intercept form. Since both equations have lines with the same slope, they are either the same line or parallel lines; either way, the system does not have exactly one solution.
The solution of a system of linear equations is the point at which their lines intersect; if they are parallel, then by definition, there is no such point, and the system has no solution.
If
In slope-intercept form:
This line has a slope of
If is modeled by , find the slope of .
I) .
II) crosses the -axis at .
If
I)
II)
Tap to see back →
I) Tells us the two lines are parallel. Parallel lines have the same slope.
II) Gives us the x-intercept of b(t). By itself this gives us no clue as to the slop of b. If we had another point on b(t) we could find the slope, but we don't have another point.
So, statement I is what we need.
I) Tells us the two lines are parallel. Parallel lines have the same slope.
II) Gives us the x-intercept of b(t). By itself this gives us no clue as to the slop of b. If we had another point on b(t) we could find the slope, but we don't have another point.
So, statement I is what we need.
Calculate the slope of a line parallel to line .
- Line passes through points and .
- The equation for line is .
Calculate the slope of a line parallel to line
- Line
- The equation for line
Tap to see back →
Statement 1: Since we're referring to a line parallel to line XY, the slopes will be identical. We can use the points provided to calculate the slope:
We can simplify the slope to just .
Statement 2: Finding the slope of a line parallel to line XY is really straightforward when given the equation of a line.
Where is the slope and the y-intercept.
In this case, our value is .\
Each statement alone is sufficient to answer the question.
Statement 1: Since we're referring to a line parallel to line XY, the slopes will be identical. We can use the points provided to calculate the slope:
We can simplify the slope to just
Statement 2: Finding the slope of a line parallel to line XY is really straightforward when given the equation of a line.
Where
In this case, our
Each statement alone is sufficient to answer the question.
Find the slope of the line parallel to .
I) passes through the point .
II) has an x-intercept of 290.
Find the slope of the line parallel to
I)
II)
Tap to see back →
Recall that parallel lines have the same slope and that slope can be calculated from any two points.
Statement I gives us a point on
Statement II gives us the x-intercept, a.k.a. the point .
Therfore, using both statements, we can find the slope of and any line parallel to it.
Recall that parallel lines have the same slope and that slope can be calculated from any two points.
Statement I gives us a point on
Statement II gives us the x-intercept, a.k.a. the point
Therfore, using both statements, we can find the slope of