Geometry Problem - GMATPREP

Statements (1) and (2) yield the exact same information; that
m=3b (where y = mx + b)

So (e)

persevering wrote:Statements (1) and (2) yield the exact same information; that
m=3b (where y = mx + b)

So (e)

Persevering ..thanks for the explanations, but I would like to understand a bit more on this problem

1. The slope of line l is 3 times its y intercept
What does this mean mathematically in an equation of line y=mx+b
y intercept is b isnt it?(putting x as 0). So does this mean m = 3b?

2.x intercept of line l is -1/3.
Does this mean -b/m = -1/3 ?

Secondly I would like to know if given the equation of a line y = 2x+3,
is this how we calculate x intercept and y intercept
y/a + x/b =1 so
y -2x = 3
=> y/3 -2x/3 =1
=> y/3 -x/(3/2) =1
=> y/3+x(-3/2) =1
so y intercept is 3
x intercept is -3/2
Am I right?

I would like to know the solution to this one too.

Calling all experts....pandey ji where are you ?

statement 1 gives you the slope of line l is 3 times its y-intercept. Knowing this fact on it's own is insufficient to finding the slope of the line, as we have no reference point. Furthermore, if line l crosses above or below the x-axis that will affect the slope making it positive or negative, depending on the reference point, which we do not have. Therefore, statement 1 is insufficient.

statement 2 gives the x-intercept but gives no hint as to how the line proceeds through that point. Going through (-1/3,0) the line could cross the y-intercept anywhere from +infinity to -infinity. Therefore insufficient.

Statements 1 and 2 taken together look like they may solve the answer. From statement 2 we know the x intercept (-1/3,0). However, does line l pass through th y-intercept at (0, 1) or (0, -1)? Both of these points would fulfill statements 1 and 2 together, there for statements 1 and 2 taken together are NOT sufficient. (E)

gmatrant wrote:
.....Secondly I would like to know if given the equation of a line y = 2x+3,
is this how we calculate x intercept and y intercept
y/a + x/b =1 so
y -2x = 3
=> y/3 -2x/3 =1
=> y/3 -x/(3/2) =1
=> y/3+x(-3/2) =1
so y intercept is 3
x intercept is -3/2
Am I right?

The x intercept of the line is the intercept the line makes on the X axis when it is extended to the X axis, now we know that for every point on the X axis the Y coordinate is 0 ... So, for any line (eg y = 2x+3), to find the X intercept substitute y = 0 .. so if u substitute y =0 in y =2x+3 we get the x intercept of the line as -3/2 ..

Similarly if you want to find the Y intercept of the line substitute x =0 in the equation of the line, if you do that in the above equation we have Y intercept of line = 3 ..

Regards.