DSQ: Calculating the slope of parallel lines - GMAT Quantitative

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.