y-intercept of line l?

gmattesttaker2 wrote:In the xy-plane, what is the y-intercept of line l?

1) The slope of line l is 3 times its y-intercept
2) The x-intercept of line l is -1/3

If the slope and y-intercept of a line in xy plane are m and c respectively, then the line can be represented by the equation y = mx + c and the x=intercept of the line will be -c/m

Statement 1: m = 3c ---> Not sufficient

Statement 2: -c/m = -1/3 ---> m = 3c ---> Not sufficient

1 & 2 Together: We have no new information ---> Not sufficient

The correct answer is E.

gmattesttaker2 wrote:
In the xy-plane, what is the y-intercept of line l?

1) The slope of line l is 3 times its y-intercept
2) The x-intercept of line l is -1/3

If you haven't memorized formulas for x-intercepts (I haven't), you don't need them here. We know that the general equation of a line is y = mx + b, where m is the slope, and b is the y-intercept. We need to find the value of b.

Neither statement is sufficient alone. From Statement 2, we know that (-1/3, 0) is a point on our line, so if we plug x = -1/3 and y = 0 into our equation, what we get will be true:

y = mx + b
0 = m(-1/3) + b
m = 3b

So if Statement 2 is true, then it must always be true that the slope is 3 times the y-intercept. That is, Statement 1 gives us no new information at all, and the answer is E.