Is the slope of line q negative?

Slope of the line is nothing but Tan of the angle it makes with x axis (right side)

Clearly both statement alone are not sufficient

Both together Line has to make an acute angle with x axis --> tan of that angle has to be positive and slope too.
So slope of line q is positive (not negative) hence ans, C

For this question, I would visualize it.

1) - negative x intercept, you could have either a positive or negative slope right? - Insufficient
2) - passes through quadrant 1, again you could have a line that is either positive or negative slope right? - Insufficient

Test together - if you choose a line that must have a negative x intercept, let's choose -5. If the slope is positive, it will pass through Quandrant 1, if the slope is negative, it cannot pass through 1 as it goes through quadrant 4. Since 2 tells you it passes through quandrant 1 - you know the slope must be positive.

So the answer is NO, the slope is positive - C, you'll need both statements.

option C

Please find attached the figure.

Hi, I thought I understood this question until I saw this image. Is the line in the last (combined) coordinate plane correct?

The y intercept is where the line crosses the y axis, right? If yes, then the line should cross the bottom part of y (the horizontal axis) at some point.

Then, if the line in the plane has to go through Q 1, it should look like in the following graph, or am I wrong? Otherwise, it is not crossing the y axis...

Hi pacifist85,

In the original prompt, Fact 1 tells us that the X-INTERCEPT of Line L is negative. In your drawing, you've made the X-intercept POSITIVE (so the drawing does not match the Facts and is incorrect).

GMAT assassins aren't born, they're made,
Rich

Oh I am sorry... Did I read y intercept instead of x intercept? Probably... Or perhaps I dragged the question into the answer choices trying to make the intercept negative and mixing everything up. Whatever I did, my bad!

Original Solution: C

Explanation by Veritas prep:

If a line has a negative x-intercept, that means that its slope and its y-intercept must share a sign: either both are negative or both are positive. (Remember that the x-intercept can be expressed as –(b/m), so if only one of those values is negative, then –(b/m) must be positive, making a positive x-intercept.) Statement (1) is thus INSUFFICIENT. Statement (2) is useless: any line can pass through Quadrant 1; INSUFFICIENT. Combine the statements and visualize the line. If the line crosses the x-axis to the left of zero, then it can only go through Quadrant I if it has a positive slope; if it had a negative slope, it would pass through Quadrants II, III, and IV. (C).

Is the slope of line q negative?

since we have intercepts, slopes and quadrants in picture, let me take the equation of line as \(\frac{x}{a}+\frac{y}{b}=1\) or \(y=-(\frac{b}{a})x+b\) where slope of the line is \(-(\frac{b}{a})\)

statement 1: Line q has a negative x-intercept.

\(a\) is negative say \(-1\) (any negative integer)
by substituting \(a=-1\) we get the equation of line as \(y=bx+b\)
but still we have no idea what is the sign of b i.e., y intercept can be either positive or negative.
if b is positive slope of line q is positive
if b is negative slope of line q is negative

thus statement 1 is insufficient.

statement 2: Line q passes through Quadrant I.
we can easily conclude that line slope can be both positive and negative.
b is positive whereas a can be negative or positive.


Now combine both statements I and II

we know that b is positive in Quadrant I and a is negative.

thus slope is always positive and never negative.

answer NO sufficient YES

Solution: C

If a line has a negative x-intercept, that means that its slope and its y-intercept must share a sign: either both are negative or both are positive. (Remember that the x-intercept can be expressed as –(b/m), so if only one of those values is negative, then –(b/m) must be positive, making a positive x-intercept.) Statement (1) is thus INSUFFICIENT.
Statement (2) is useless: any line can pass through Quadrant 1; INSUFFICIENT. Combine the statements and visualize the line. If the line crosses the x-axis to the left of zero, then it can only go through Quadrant I if it has a positive slope; if it had a negative slope, it would pass through Quadrants II, III, and IV. (C).

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