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Does line Ax + By + C = 0 (A is not 0) intersect the x-axis on the negative side?

1. BA <0> 0

Please explain your answer.

Getting E.

Ax + By + C = 0
By = -Ax - C (cannot divide by B just yet since B could be 0)

Stat 1:
Tells us that B is not 0 and that A and B have the same sign.
y = - (A/B)x - C
To find x, y = 0:
-(A/B)x = C
x = -(B/A) * C
B/A will have the same sign therefore -(B/A) will be negative which makes me think that the answer to the stem is yes. However, what if C = 0? The answer to the stem is no. Insuff.

Stat 2:
Tells us that A & C have opposite signs. I don't think that this alone helps us in determine the answer. Insuff.

Together:
If A is +ve and C is -ve then x intercept is +ve
If A is -ve and C is +ve then x intercept is -ve
Insuff.

Re: Does line Ax + By + C = 0 (A is not 0) intersect the x-axis [#permalink]
12 Nov 2013, 22:23

@laserglare

Yes, to find the x-intercept of a line, the point where it intersects the x-axis, we set the y-coordinate to 0. You correctly replaced y as 0 in the equation Ax+By+C=0, which gave you the x-intercept of -C/A.

Here 2 alone is sufficient because if AC>0, then we have either both A and C are positive or both A and C are negative, in both scenarios -C/A is negative, meaning the x-intercept is negative or intersects the x-axis to the left of the origin.

Re: Does line Ax + By + C = 0 (A is not 0) intersect the x-axis [#permalink]
12 Nov 2013, 22:29

1

This post received KUDOS

Expert's post

laserglare wrote:

i was doing this on the gmatclub tests and i cannot figure out why all we need is x = -c/a

"So, the x-intercept of line ax+by+c=0 is x=−c/a." I plugged in 0 so ax+ by+ c = 0 then y = ( -ax - c ) / b

was i supposed to think of this question like this ax + b (0) + c = 0 ax + c = 0 x = -c/a

then use that equation to figure out what x is???

(when i was doing this before viewing the solution, i assumed that we would need a/b to solve because -a/b * x.)

Given Ax + By + C = 0 is the equation of a line. You need to figure out whether it intersects x axis on the negative side i.e. in the second quadrant. You want to know that when the line crosses the x axis (if it does), is x co-ordinate negative there? When does a line cross the x axis? When its y co-ordinate is 0. So how will you know the point where the line crosses the x axis? You put y = 0. Ax + B*0 + C = 0 x = -C/A So when y = 0, x = -C/A

We want to know whether this x cor-ordinate (-C/A) is negative. It will be negative when C/A is positive i.e. both C and A will have the same sign (either both positive or both negative) Statement 2 tells you that C and A have the same sign (since their product is positive). Hence it is enough alone.

Re: Does line Ax + By + C = 0 (A is not 0) intersect the x-axis [#permalink]
13 Nov 2013, 01:04

1

This post received KUDOS

Expert's post

1

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bmwhype2 wrote:

Does line Ax + By + C = 0 (A is not 0) intersect the x-axis on the negative side?

(1) BA < 0. (2) AC > 0.

M18-13

Does line Ax + By + C = 0 (A is not 0) intersect the x-axis on the negative side?

\(ax+by+c=0\) is equation of a line. Note that the line won't have interception with x-axis when \(a=0\) (and \(c\neq{0}\)): in this case the line will be \(y=-\frac{c}{b}\) and will be parallel to x -axis.

Now, in other cases (when \(a\neq{0}\)) x-intercept of a line will be the value of \(x\) when \(y=0\), so the value of \(x=-\frac{c}{a}\). Question basically asks whether this value is negative, so question asks is \(-\frac{c}{a}<0\)? --> is \(\frac{c}{a}>0\)? --> do \(c\) and \(a\) have the same sign?

(1) BA < 0. Not sufficient as we can not answer whether \(c\) and \(a\) have the same sign. (2) AC > 0 --> \(c\) and \(a\) have the same sign. Sufficient.

Re: Does line Ax + By + C = 0 (A is not 0) intersect the x-axis [#permalink]
03 Feb 2015, 16:08

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