DSQ: Calculating the equation of a parallel line - GMAT Quantitative Reasoning
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Data Sufficiency Question
What is the slope of a line that passes through the point (2,3)?
1. It passes through the origin
2. It does not intersect with the line 
Data Sufficiency Question
What is the slope of a line that passes through the point (2,3)?
1. It passes through the origin
2. It does not intersect with the line
In order to calculate the equation of a line that passes through a point, we need one of two pieces of information. If we know another point, we can calculate the slope and solve for the 
-intercept, giving us the equation of the line. Alternatively, if we know the slope (which we can conclude from the parallel line in statement 2) we can calculate the 
-intercept and determine the equation of the line.
In order to calculate the equation of a line that passes through a point, we need one of two pieces of information. If we know another point, we can calculate the slope and solve for the
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Find the equation of the line parallel to the following line:
I) The new line passes through the point 
.
II) The new line has a 
-intercept of 
.
Find the equation of the line parallel to the following line:
I) The new line passes through the point
II) The new line has a
To find the equation of a parallel line, we need the slope and the y-intercept.
Parallel lines have the same slope, so we have that.
I and II each give us a point on the graph, so we could find the equation of the line through either of them.
To find the equation of a parallel line, we need the slope and the y-intercept.
Parallel lines have the same slope, so we have that.
I and II each give us a point on the graph, so we could find the equation of the line through either of them.
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Find the equation of the line 
.
- The slope of line
is 
.
- Line
goes through point 
.
Find the equation of the line
- The slope of line
- Line
Statement 1: We're given the slope line AB, because we are ask for the equation of the line we need more than just the slope of the line. Therefore, this information alone is not sufficient to write an actual equation.
Statement 2: Using the information from statement 1 and the points provided in this statement, we can answer the question.
Statement 1: We're given the slope line AB, because we are ask for the equation of the line we need more than just the slope of the line. Therefore, this information alone is not sufficient to write an actual equation.
Statement 2: Using the information from statement 1 and the points provided in this statement, we can answer the question.
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Given 
, find the equation of 
.
I) 
II) 
passes through the point 
Given
I)
II)
We are asked to find the equation of a line related to another line.
Statement I tells us the two lines are parallel. This means they have the same slope
Statement II gives us a point on our desired line. We can use this to find the line's y-intercept, which will then allow us to write its equation.
Plug all of the given info into slope-intercept form and solve for b, the line's y-intercept:
So our equation is:
We are asked to find the equation of a line related to another line.
Statement I tells us the two lines are parallel. This means they have the same slope
Statement II gives us a point on our desired line. We can use this to find the line's y-intercept, which will then allow us to write its equation.
Plug all of the given info into slope-intercept form and solve for b, the line's y-intercept:
So our equation is:
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