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84% (00:48) correct
16%
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In the xy-plane, what is the slope of line l that passes through the point (1,1)?
(1) The x-intercept of line l is 2.
(2) The y-intercept of line l is 2.
(1) The x-intercept of line l is 2.
(2) The y-intercept of line l is 2.
02 May 2022, 08:17
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Step 1: Analyse Question Stem
A line l passes through the point (1,1).
We have to find the slope of this line l.
To do this, the most convenient form of the equation of a straight line to use, is the slope intercept form i.e. y = mx + c, where m is the slope of the line.
Note that other forms of the equation can always be converted to this form to help us find the slope of the line.
However, what is more important is to understand the concept of ‘Unique figure’. In a Data Sufficiency question on Geometry, any information that gives you a unique figure is sufficient data.
Therefore, as long as any information tells us that there is ONE definite line through (1,1), that information is sufficient.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: The x-intercept of line l is 2.
This means that the line passes through (2,0). From the question, we also know that the line passes through (1,1).
There is ONE and ONLY one line which can pass through any two points.
If there is one unique line, the slope of this line (l) can be calculated.
The data in statement 1 is sufficient to find the slope of line l.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: The y-intercept of line l is 2.
This means that the line passes through (0, 2). From the question, we also know that the line passes through (1,1).
Again, we have ONE line which can pass through these points. Therefore, the slope of this line (l) can be calculated.
The data in statement 2 is sufficient to find the slope of line l.
Statement 2 alone is sufficient. Answer option A can be eliminated.
The correct answer option is D.
A line l passes through the point (1,1).
We have to find the slope of this line l.
To do this, the most convenient form of the equation of a straight line to use, is the slope intercept form i.e. y = mx + c, where m is the slope of the line.
Note that other forms of the equation can always be converted to this form to help us find the slope of the line.
However, what is more important is to understand the concept of ‘Unique figure’. In a Data Sufficiency question on Geometry, any information that gives you a unique figure is sufficient data.
Therefore, as long as any information tells us that there is ONE definite line through (1,1), that information is sufficient.
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE
Statement 1: The x-intercept of line l is 2.
This means that the line passes through (2,0). From the question, we also know that the line passes through (1,1).
There is ONE and ONLY one line which can pass through any two points.
If there is one unique line, the slope of this line (l) can be calculated.
The data in statement 1 is sufficient to find the slope of line l.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: The y-intercept of line l is 2.
This means that the line passes through (0, 2). From the question, we also know that the line passes through (1,1).
Again, we have ONE line which can pass through these points. Therefore, the slope of this line (l) can be calculated.
The data in statement 2 is sufficient to find the slope of line l.
Statement 2 alone is sufficient. Answer option A can be eliminated.
The correct answer option is D.
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