ds - coordinate geometry 2

[ccassel]

Hi,

How would you answer this question?

In the xy-plane, the line with equation ax+by+c=0, where abc(does not equal)0, has a slope of 2/3. What is the value of b?

(1) a=4
(2) c=-6

Cheers,

[MAAJ]

IMO [spoiler](A)[/spoiler]

In the xy-plane, the line with equation ax+by+c=0, where abc(does not equal)0, has a slope of 2/3. What is the value of b?

ax + by + c = 0
by = -ax - c
y = (-ax - c)/b
y = (-a/b)x - (c/b)
(-a/b) -> must be the slope

(1) a=4
-a/b = -4/b
-4/b = 2/3
-12 = 2b
b = -6 Sufficient

(2) c=-6
y = (-a/b)x - (c/b)
y = (2/3)x - (c/b)
y = (2/3)x - (-6/b)
I believe this is insufficient, because we don't know the value of x and y, and we can't say that b=3 from -a/b = 2/3

What's the OA???

Hi,

How would you answer this question?

In the xy-plane, the line with equation ax+by+c=0, where abc(does not equal)0, has a slope of 2/3. What is the value of b?

(1) a=4
(2) c=-6

Cheers,

[ccassel]

Answer choice A is correct.

Cheers,

[tpr-becky]

This is a coordinate geometry question with a line equation - which means that the slope is equal to the variable m in the y = mx + b standard equation - so first we have to get things to that format.

by manipulating this equation we get y = (-a(x) + c)/b - therefore the slope is -a/b. since the problem tells you that the slope is 2/3 that means that -a/b =2/3

1. if we plug in 4 for a we can quickly find b - so AD are left

2. c plays no role in the slope formula so A is the answer.

Best of Luck