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Coordinate Geometry

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by [email protected] » Thu Jan 30, 2014 7:29 pm
A line is graphed on a coordinate plane. How many times less is the distance between the y-intercept and the x-axis than the distance between the x-intercept and the y-axis?

1.The slope of the line is −9/13.


2.The y-intercept is located at (0, 26).
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Source: — Data Sufficiency |

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by [email protected] » Thu Jan 30, 2014 11:44 pm
Hi shibsriz,

This DS question looks far more complex than it is. The "secret" behind it is in understanding what the question is "really" asking you to figure out.

Here, we're asked how many times less is (the distance from the y-intercept to the x-axis) and (the distance from the x-intercept to the y-axis)?

These two calculations can be rewritten as (distance from y-intercept to point 0,0) and (distance from x-intercept to point 0,0)....

Conceptually, this relationship is referred to as "change in Y over change in X", otherwise known as SLOPE.

This DS question is asking what the slope of the line is...

Fact 1: Slope of the line is -9/13
This answers the question.
Fact 1 is SUFFICIENT

Fact 2: The Y-intercept is (0,26)
Without the X-intercept, we have no way of figuring out the slope.
Fact 2 is INSUFFICIENT

Final Answer: A

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by sanju09 » Fri Jan 31, 2014 3:41 am
[email protected] wrote:A line is graphed on a coordinate plane. How many times less is the distance between the y-intercept and the x-axis than the distance between the x-intercept and the y-axis?

1.The slope of the line is −9/13.


2.The y-intercept is located at (0, 26).
It's of great help to rephrase the complex wordings to the easy one before anything. For example "the distance between the y-intercept and the x-axis" simply means the 'y-intercept', and "the distance between the x-intercept and the y-axis" simply means the 'x-intercept'. Now, the rephrased question is:

A line is graphed on a coordinate plane. How many times less is the y-intercept than the x-intercept of the line?

(1) We know that the slope of a line also equals to -y-intercept/x-intercept, and if -y-intercept/x-intercept = -9/13, then we know the ratio between the two quantities and the question can be answered. Sufficient

(2) Location of y-intercept only doesn't answer the slope or any other requirement of the question, [spoiler]hence insufficient.

Pick A[/spoiler]
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