rajatvmittal wrote:A line is graphed on a coordinate plane. How many times less is the distance between the y-intercept and the x-axis than the distance between the x-intercept and the y-axis?
The slope of the line is -9/13.
The y-intercept is located at (0, 26).
It makes no grammatical or mathematical sense to ask "how many times less" one thing is than another. The question also needs to make clear that the x and y-intercepts of the line are not both at (0,0). So the question is not well-written. I think it means to ask for the ratio between the distance from the origin to the y-intercept, and the distance between the origin and the x-intercept. So if b is the y-intercept and c is the x-intercept, I think the question is asking if you can find |b|/|c|.
In that case, Statement 2 is clearly not sufficient. It should also be clear that both statements would be sufficient together - after all, with both statements, we know exactly what the line looks like, so we could answer any question at all about it. That's too obvious, so you should suspect that Statement 1 is sufficient alone, and it is.
If a line has the equation y=mx + b, where m is the slope and b is the y-intercept, then we can work out the x-intercept of the line by plugging in y=0:
0 = mx+b
x = -b/m
So the y-intercept is b, and the x-intercept is -b/m. Notice if we divide the y-intercept by the x-intercept we just get b/(-b/m) = -m. So we only need the slope of the line to find |b|/|c| here; it is equal to 9/13, and Statement 1 is sufficient.
