Source: Official Guide Revised GRE 1st Ed. Part 8; Section 6; #11

1

In the xy-plane, line k is a

In the xy-plane, line k is a line that does not pass through the origin. Which of the following statements individually provide(s) sufficient additional information to determine whether the slope of line k is negative? Indicate all such statements. The x-intercept of line k is twice the y-intercept of line k., The product of the x-intercept and the y-intercept of line k is positive., Line k passes through the points (a, b) and (r, s), where (a ? r)(b ? s) 0. 12

2 Explanations

1

sourov datta

Thanks Chris . Nice explanation .

Jul 1, 2016 • Comment

Cydney Seigerman, Magoosh Tutor

On behalf of Chris, you're very welcome :D Happy studying!

Jul 4, 2016 • Reply

3

Gravatar Chris Lele, Magoosh Tutor

Oct 11, 2012 • Comment

Damien Sighaka

Hello, thanks for your explanations nevertheless i dont understand why the x intercept is twice the y intercept: If the line was crossing the y axis at 4, and the x axis at one, it would still have a negative slope but a different ratio between x and y...

Jun 28, 2017 • Reply

Sam Kinsman, Magoosh Tutor

Hi Damien,

You're right that if a line crosses the y axis at 4 and the x axis at 1, it has a negative slope - but the x intercept is NOT twice the y intercept. That's correct!

However, the question is not asking us whether ALL lines with a negative slope will have an x intercept that is twice the y intercept.

You could think of the question as saying this: "consider all the lines that have an x intercept that is twice the y intercept. Do all of these lines have the same kind of slope (positive or negative)?"

In the video, Mike shows that all of the lines that have an x intercept that is twice the y intercept must be lines with a negative slope. Therefore, if we know that a line has an x intercept that is twice the y intercept, we have enough information to determine that it has a negative slope.

I hope that clarifies!

Best,
Sam

Jul 6, 2017 • Reply

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