Before I answer YOUR question, I shall answer THIS problem.

In the xy-plane, the line with equation ax + by + c = 0, where abc ≠ 0, has slope of 2/3
What is the value of b ?
A line equation can be written in te form of y = mx + d where m is the slope of the line and d the Y intercept. The equation ax + by + c = 0 can be written as y = (-a/b)x -(c/b).
Slope of the equation is m = -a/b = 2/3

(1) a = 4

m = -a/b = -4/b = 2/3 ; b = -6 Sufficient!

(2) c = -6

Oops Insufficient!

factor26 wrote:i started the question by breaking down the equation into y=mx+b format and found that y= -a/b - c/b ,my cousion here is since we are given the slope of 2/3 ... shouldnt the value of b be equal to 3? Am i missing something here? please help!

So you say -a/b = 2/3 then b = 3?. No it isn't.
If a = -2 and -a/b = 2/3, then b = 3(Ok wait a sec)
If a = -4 and -a/b =2/3, then b = 6 (Oops)
If a = 4 and -a/b =2/3, then b = -6 (Oops)

Since Slope m =-a/b is a ratio, we cannot equate the numerator of the left hand side to the numerator of the right hand side(Same rule applies to the Denominator)

factor26 wrote:In the xy-plane, the line with equation ax + by + c = 0,
where abc ≠ 0, has slope of 2/3

What is the value of b ?
(1) a = 4
(2) c = -6

OG Answer is a

i started the question by breaking down the equation into y=mx+b format and found that y= -a/b - c/b

my cousion here is since we are given the slope of 2/3 ... shouldnt the value of b be equal to 3?

am i missing something here? please help!

Converting ax + by + c = 0 into y=mx + b:
by = -ax - c
y = (-a/b)x - c/b.

Since the slope of the line is 2/3:
-a/b = 2/3
a/b = -2/3.

This gives us the RELATIONSHIP between a and b but not the EXACT VALUES of a and b.
It's possible that a=-2 and b=3.
It's possible that a=-4 and b=6, since -4/6 = -2/3.
a and b can any values such that a/b = -2/3.
To determine the EXACT VALUE of b, we need to know the exact value of a.

Question rephrased: What is a?

Statement 1: a=4.
SUFFICIENT.

Statement 2: c=-6.
No way to determine the value of b.
INSUFFICIENT.

The correct answer is A.

factor26 wrote:In the xy-plane, the line with equation ax + by + c = 0,
where abc ≠ 0, has slope of 2/3

What is the value of b ?
(1) a = 4
(2) c = -6

OG Answer is a

i started the question by breaking down the equation into y=mx+b format and found that y= -a/b - c/b

my cousion here is since we are given the slope of 2/3 ... shouldnt the value of b be equal to 3?

am i missing something here? please help!

ax + by + c = 0
slope of an equation is given as
m = -(coefficient of x)/(coefficient of y)

for this equation
ax + by + c = 0
the slope would be
m = -a/b