rahul16singh28 wrote:

Bunuel wrote:

In the xy-plane, if line m has negative slope and passes through the point (r, 6), is the x-intercept of line m positive?

(1) The slope of line m is -1/2

(2) r > 0

Let the equation of the line be y = mx + c, where m is slope. Here, X & Y-Intercept is X = -c/m, Y = c. The question = Is -c/m positive.

1) As the line passes through (r,6) implies, c = 6.. As m is negative X intercept will be positive... So, Sufficient.

2) As r > 0, 6 = rm + c. Now, X = -c/m or -(6-rm)/c --> rm-6/m --> r - (6/m)... As m is -ve and r>0, X intercept will be positive.

Hence, D.

Hi Rahul

The fact that line passes through (r, 6) doesn't necessarily imply that c (or y intercept) is 6 (your first statement analysis). Eg, if r = 6, then we only have the data that this line passes through the point (6,6). Now this line could also pass through the origin, in which case the y intercept of this line will be 0. OR this line passing through the point (6,6) could also pass through a point (0, -2) in which case y intercept of this line will be negative.

If we were given that r=0, then we should have concluded that the line is passing through (0,6) and thus its y intercept is 6.